Automatica
Journal Prestige (SJR): 3.896 Citation Impact (citeScore): 7 Number of Followers: 11 Hybrid journal (It can contain Open Access articles) ISSN (Print) 00051098 Published by Elsevier [3162 journals] 
 Stability analysis of networked linear control systems with
directfeedthrough terms Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Stefan Heijmans, Romain Postoyan, Dragan Nešić, Navid Noroozi, Maurice Heemels We consider networked control systems (NCSs) composed of a linear plant and a linear controller interconnected by packetbased communication channels with communication constraints. We are interested in the setup where directfeedthrough terms are present in the plant and/or in the controller, a case that is largely ignored in the literature due to its inherent complexity and counterintuitive results in the analysis despite its relevance for important classes of controllers including Proportional–Integral (PI) regulators. This setup calls for a novel stability analysis, for which we take a renewed look at the concept of uniformly globally exponentially stable (UGES) scheduling protocols that turned out to be instrumental in earlier approaches. We provide a generalization of the UGES property, called (DP,DC)UGES with DP∕DC being the directfeedthrough matrices of the plant/controller, respectively, and we present generic conditions on these directfeedthrough terms DP∕DC such that the classical UGES property of scheduling protocols implies (DP,DC)UGES. This allows us to derive conditions leading to a maximally allowable transmission interval (MATI) such that stability of the overall NCS is guaranteed. In addition, it is shown that it is possible to get more tailored results for the wellknown sampleddata (SD), roundrobin (RR), and tryoncediscard (TOD) protocols leading to less conservative conditions on the directfeedthrough terms than the generic ones. We also introduce new (DP,DC)UGES scheduling protocols, designed to handle the directfeedthrough terms in a more effective way than existing protocols. Our results are illustrated using the example of a batch reactor.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Stefan Heijmans, Romain Postoyan, Dragan Nešić, Navid Noroozi, Maurice Heemels We consider networked control systems (NCSs) composed of a linear plant and a linear controller interconnected by packetbased communication channels with communication constraints. We are interested in the setup where directfeedthrough terms are present in the plant and/or in the controller, a case that is largely ignored in the literature due to its inherent complexity and counterintuitive results in the analysis despite its relevance for important classes of controllers including Proportional–Integral (PI) regulators. This setup calls for a novel stability analysis, for which we take a renewed look at the concept of uniformly globally exponentially stable (UGES) scheduling protocols that turned out to be instrumental in earlier approaches. We provide a generalization of the UGES property, called (DP,DC)UGES with DP∕DC being the directfeedthrough matrices of the plant/controller, respectively, and we present generic conditions on these directfeedthrough terms DP∕DC such that the classical UGES property of scheduling protocols implies (DP,DC)UGES. This allows us to derive conditions leading to a maximally allowable transmission interval (MATI) such that stability of the overall NCS is guaranteed. In addition, it is shown that it is possible to get more tailored results for the wellknown sampleddata (SD), roundrobin (RR), and tryoncediscard (TOD) protocols leading to less conservative conditions on the directfeedthrough terms than the generic ones. We also introduce new (DP,DC)UGES scheduling protocols, designed to handle the directfeedthrough terms in a more effective way than existing protocols. Our results are illustrated using the example of a batch reactor.
 A necessary and sufficient condition for local asymptotic stability of a
class of nonlinear systems in the critical case Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Jiandong Zhu, Chunjiang Qian By the theory of linear differential equations, a system described by a chain of integrators with a linear feedback is globally asymptotically stable if and only if the characteristic polynomial is Hurwitz, which implies that all the coefficients in the linear feedback equation are negative. However, negative coefficients may not guarantee the local asymptotic stability of the linear system. In this paper, we reveal that, by monotonizing the powers of the integrators, the strict negativity of the feedback coefficients is not only necessary but also sufficient for the local asymptotic stability of the system. A dual result is also obtained for the dual power integrator systems.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Jiandong Zhu, Chunjiang Qian By the theory of linear differential equations, a system described by a chain of integrators with a linear feedback is globally asymptotically stable if and only if the characteristic polynomial is Hurwitz, which implies that all the coefficients in the linear feedback equation are negative. However, negative coefficients may not guarantee the local asymptotic stability of the linear system. In this paper, we reveal that, by monotonizing the powers of the integrators, the strict negativity of the feedback coefficients is not only necessary but also sufficient for the local asymptotic stability of the system. A dual result is also obtained for the dual power integrator systems.
 Price of anarchy in electric vehicle charging control games: When Nash
equilibria achieve social welfare Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Luca Deori, Kostas Margellos, Maria Prandini We consider the problem of optimal charging of plugin electric vehicles (PEVs). We treat this problem as a multiagent game, where vehicles/agents are heterogeneous since they are subject to possibly different constraints. Under the assumption that electricity price is affine in total demand, we show that, for any finite number of heterogeneous agents, the PEV charging control game admits a unique Nash equilibrium, which is the optimizer of an auxiliary minimization program. We are also able to quantify the asymptotic behaviour of the price of anarchy for this class of games. More precisely, we prove that if the parameters defining the constraints of each vehicle are drawn randomly from a given distribution, then, the value of the game converges almost surely to the optimum of the cooperative problem counterpart as the number of agents tends to infinity. In the case of a discrete probability distribution, we provide a systematic way to abstract agents in homogeneous groups and show that, as the number of agents tends to infinity, the value of the game tends to a deterministic quantity.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Luca Deori, Kostas Margellos, Maria Prandini We consider the problem of optimal charging of plugin electric vehicles (PEVs). We treat this problem as a multiagent game, where vehicles/agents are heterogeneous since they are subject to possibly different constraints. Under the assumption that electricity price is affine in total demand, we show that, for any finite number of heterogeneous agents, the PEV charging control game admits a unique Nash equilibrium, which is the optimizer of an auxiliary minimization program. We are also able to quantify the asymptotic behaviour of the price of anarchy for this class of games. More precisely, we prove that if the parameters defining the constraints of each vehicle are drawn randomly from a given distribution, then, the value of the game converges almost surely to the optimum of the cooperative problem counterpart as the number of agents tends to infinity. In the case of a discrete probability distribution, we provide a systematic way to abstract agents in homogeneous groups and show that, as the number of agents tends to infinity, the value of the game tends to a deterministic quantity.
 Opinion dynamics in social networks with stubborn agents: An issuebased
perspective Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Ye Tian, Long Wang Classic models on opinion dynamics usually focus on a group of agents forming their opinions interactively over a single issue. Yet generally agreement cannot be achieved over a single issue when agents are not completely open to interpersonal influence. In this paper, opinion formation in social networks with stubborn agents is considered over issue sequences. The social network with stubborn agents is described by the Friedkin–Johnsen (F–J) model where agents are stubborn to their initial opinions. Firstly, we propose a sufficient and necessary condition in terms of network topology for convergence of the F–J model over a single issue. Secondly, opinion formation of the F–J model is investigated over issue sequences. Our analysis establishes connections between the interpersonal influence network and the network describing the relationship of agents’ initial opinions for successive issues. Taking advantage of these connections, we derive the sufficient and necessary condition for the F–J model to achieve opinion consensus and form clusters over issue sequences, respectively. Finally, we consider a more general scenario where each agent has bounded confidence in forming its initial opinion. By analyzing the evolution of agents’ ultimate opinions for each issue over issue sequences, we prove that the connectivity of the statedependent network is preserved in this setting. Then the conditions for agents to achieve opinion consensus over issue sequences are established. Simulation examples are provided to illustrate the effectiveness of our theoretical results.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Ye Tian, Long Wang Classic models on opinion dynamics usually focus on a group of agents forming their opinions interactively over a single issue. Yet generally agreement cannot be achieved over a single issue when agents are not completely open to interpersonal influence. In this paper, opinion formation in social networks with stubborn agents is considered over issue sequences. The social network with stubborn agents is described by the Friedkin–Johnsen (F–J) model where agents are stubborn to their initial opinions. Firstly, we propose a sufficient and necessary condition in terms of network topology for convergence of the F–J model over a single issue. Secondly, opinion formation of the F–J model is investigated over issue sequences. Our analysis establishes connections between the interpersonal influence network and the network describing the relationship of agents’ initial opinions for successive issues. Taking advantage of these connections, we derive the sufficient and necessary condition for the F–J model to achieve opinion consensus and form clusters over issue sequences, respectively. Finally, we consider a more general scenario where each agent has bounded confidence in forming its initial opinion. By analyzing the evolution of agents’ ultimate opinions for each issue over issue sequences, we prove that the connectivity of the statedependent network is preserved in this setting. Then the conditions for agents to achieve opinion consensus over issue sequences are established. Simulation examples are provided to illustrate the effectiveness of our theoretical results.
 Modelbased fault identification of discrete event systems using partially
observed Petri nets Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Guanghui Zhu, Zhiwu Li, Naiqi Wu This paper deals with the problem of fault identification in a system. The system is originally modeled by a Petri net, called a nominal (faultfree) net, and faults are considered as unobservable transitions not contained in the nominal net. It is assumed that partial places of the nominal net are observable and the output of the system is defined as an observed evolution, i.e., a sequence involving transitions and markings of the observable places. When faults occur, the observed evolution cannot be generated by the nominal net. We provide an approach that identifies unobservable transitions by constructing and solving an Integer Linear Programming problem according to the observed evolution and the nominal net. A faulty net is obtained by adding the identified unobservable transitions to the nominal one such that it coincides with the observed evolution. In addition, two methods to ensure acyclicity of the identified subnet, i.e., a net that includes unobservable transitions only, are reported.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Guanghui Zhu, Zhiwu Li, Naiqi Wu This paper deals with the problem of fault identification in a system. The system is originally modeled by a Petri net, called a nominal (faultfree) net, and faults are considered as unobservable transitions not contained in the nominal net. It is assumed that partial places of the nominal net are observable and the output of the system is defined as an observed evolution, i.e., a sequence involving transitions and markings of the observable places. When faults occur, the observed evolution cannot be generated by the nominal net. We provide an approach that identifies unobservable transitions by constructing and solving an Integer Linear Programming problem according to the observed evolution and the nominal net. A faulty net is obtained by adding the identified unobservable transitions to the nominal one such that it coincides with the observed evolution. In addition, two methods to ensure acyclicity of the identified subnet, i.e., a net that includes unobservable transitions only, are reported.
 Delayed point control of a reaction–diffusion PDE under
discretetime point measurements Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Anton Selivanov, Emilia Fridman We consider stabilization problem for reaction–diffusion PDEs with point actuations subject to a known constant delay. The point measurements are sampled in time and transmitted through a communication network with a timevarying delay. To compensate the input delay, we construct an observer for the future value of the state. Using a timevarying observer gain, we ensure that the estimation error vanishes exponentially with a desired decay rate if the delays and sampling intervals are small enough while the number of sensors is large enough. The convergence conditions are obtained using a Lyapunov–Krasovskii functional, which leads to linear matrix inequalities (LMIs). We design outputfeedback point controllers in the presence of input delays using the above observer. The boundary controller is constructed using the backstepping transformation, which leads to a target system containing the exponentially decaying estimation error. The indomain point controller is designed and analysed using an improved Wirtingerbased inequality. We show that both controllers can guarantee the exponential stability of the closedloop system with an arbitrary decay rate smaller than that of the observer’s estimation error.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Anton Selivanov, Emilia Fridman We consider stabilization problem for reaction–diffusion PDEs with point actuations subject to a known constant delay. The point measurements are sampled in time and transmitted through a communication network with a timevarying delay. To compensate the input delay, we construct an observer for the future value of the state. Using a timevarying observer gain, we ensure that the estimation error vanishes exponentially with a desired decay rate if the delays and sampling intervals are small enough while the number of sensors is large enough. The convergence conditions are obtained using a Lyapunov–Krasovskii functional, which leads to linear matrix inequalities (LMIs). We design outputfeedback point controllers in the presence of input delays using the above observer. The boundary controller is constructed using the backstepping transformation, which leads to a target system containing the exponentially decaying estimation error. The indomain point controller is designed and analysed using an improved Wirtingerbased inequality. We show that both controllers can guarantee the exponential stability of the closedloop system with an arbitrary decay rate smaller than that of the observer’s estimation error.
 Global stabilisation of underactuated mechanical systems via PID
passivitybased control Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Jose Guadalupe Romero, Alejandro Donaire, Romeo Ortega, Pablo Borja In this note we identify a class of underactuated mechanical systems whose desired constant equilibrium position can be globally stabilised with the ubiquitous PID controller. The class is characterised via some easily verifiable conditions on the systems inertia matrix and potential energy function, which are satisfied by many benchmark examples. The design proceeds in two main steps, first, the definition of two new passive outputs whose weighted sum defines the signal around which the PID is added. Second, the observation that it is possible to construct a Lyapunov function for the desired equilibrium via a suitable choice of the aforementioned weights and the PID gains.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Jose Guadalupe Romero, Alejandro Donaire, Romeo Ortega, Pablo Borja In this note we identify a class of underactuated mechanical systems whose desired constant equilibrium position can be globally stabilised with the ubiquitous PID controller. The class is characterised via some easily verifiable conditions on the systems inertia matrix and potential energy function, which are satisfied by many benchmark examples. The design proceeds in two main steps, first, the definition of two new passive outputs whose weighted sum defines the signal around which the PID is added. Second, the observation that it is possible to construct a Lyapunov function for the desired equilibrium via a suitable choice of the aforementioned weights and the PID gains.
 Robust Kalman filtering for twodimensional systems with multiplicative
noises and measurement degradations: The finitehorizon case Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Jinling Liang, Fan Wang, Zidong Wang, Xiaohui Liu In this paper, robust Kalman filtering problem is investigated for a class of twodimensional (2D) shiftvarying uncertain systems with both additive and multiplicative noises over a finite horizon. The measurement outputs suffer from randomly occurring degradations obeying certain probabilistic distributions, and the normbounded parameter uncertainties enter into both the state and the output matrices. The main aim of this paper is to design a robust Kalman filter such that, in the presence of parameter uncertainties and degraded measurements, certain upper bound of the generalized estimation error variance is locally minimized in the trace sense at each shift step. Recursion of the generalized estimation error variances for the addressed 2D system is first established via the introduction of a 2D identity quadratic filter, based on which an upper bound of the generalized estimation error variance is obtained. Subsequently, such an upper bound is minimized in the trace sense by properly designing the filter parameters. The design scheme of the robust Kalman filter is presented in terms of two Riccatilike difference equations which can be recursively computed for programmed applications. Finally, a numerical example is provided to demonstrate effectiveness of the proposed filter design method.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Jinling Liang, Fan Wang, Zidong Wang, Xiaohui Liu In this paper, robust Kalman filtering problem is investigated for a class of twodimensional (2D) shiftvarying uncertain systems with both additive and multiplicative noises over a finite horizon. The measurement outputs suffer from randomly occurring degradations obeying certain probabilistic distributions, and the normbounded parameter uncertainties enter into both the state and the output matrices. The main aim of this paper is to design a robust Kalman filter such that, in the presence of parameter uncertainties and degraded measurements, certain upper bound of the generalized estimation error variance is locally minimized in the trace sense at each shift step. Recursion of the generalized estimation error variances for the addressed 2D system is first established via the introduction of a 2D identity quadratic filter, based on which an upper bound of the generalized estimation error variance is obtained. Subsequently, such an upper bound is minimized in the trace sense by properly designing the filter parameters. The design scheme of the robust Kalman filter is presented in terms of two Riccatilike difference equations which can be recursively computed for programmed applications. Finally, a numerical example is provided to demonstrate effectiveness of the proposed filter design method.
 Robust discerning controls for the operating modes of linear switched
systems subject to bounded unknown inputs Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Koffi M. Djidula Motchon, Komi Midzodzi Pekpe, JeanPhilippe Cassar A linear switched system with bounded unknown inputs is considered in this paper. The study of the controlled distinguishability (or discernibility) property of the operating modes of the system is addressed. This property ensures the existence of a control input that generates different output signals of the modes regardless of the initial state vector and the unknown inputs. Such control inputs are called discerning controls. The robustness problem of the discerning controls with respect to the unknown inputs is analyzed, namely: under which conditions does a discerning control of the unknowninputfree modes remains a discerning control for the perturbed modes' To solve this problem, the existence of a quantifier measuring the size of the unknown inputs that discerning controls of the unknowninputfree modes have to be robust to in order to remain discerning controls for the perturbed modes is shown. In addition to this robustness result, an algorithm is proposed to design discerning controls for perturbed modes. Finally, from this input design procedure it is proven that when bounded unknown inputs are considered, there is an equivalence between controlled distinguishability of the unknowninputfree modes and that of the perturbed modes.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Koffi M. Djidula Motchon, Komi Midzodzi Pekpe, JeanPhilippe Cassar A linear switched system with bounded unknown inputs is considered in this paper. The study of the controlled distinguishability (or discernibility) property of the operating modes of the system is addressed. This property ensures the existence of a control input that generates different output signals of the modes regardless of the initial state vector and the unknown inputs. Such control inputs are called discerning controls. The robustness problem of the discerning controls with respect to the unknown inputs is analyzed, namely: under which conditions does a discerning control of the unknowninputfree modes remains a discerning control for the perturbed modes' To solve this problem, the existence of a quantifier measuring the size of the unknown inputs that discerning controls of the unknowninputfree modes have to be robust to in order to remain discerning controls for the perturbed modes is shown. In addition to this robustness result, an algorithm is proposed to design discerning controls for perturbed modes. Finally, from this input design procedure it is proven that when bounded unknown inputs are considered, there is an equivalence between controlled distinguishability of the unknowninputfree modes and that of the perturbed modes.
 Representation and network synthesis for a class of mixed
quantum–classical linear stochastic systems Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Shi Wang, Hendra I. Nurdin, Guofeng Zhang, Matthew R. James The purpose of this paper is to present a network realization theory for a class of mixed quantum–classical linear stochastic systems. Two forms, the standard form and the general form, of this class of linear mixed quantum–classical systems are proposed. Necessary and sufficient conditions for their physical realizability are derived. Based on these physical realizability conditions, a network synthesis theory for this class of linear mixed quantum–classical systems is developed, which clearly exhibits the quantum component, the classical component, and their interface. An example is used to illustrate the theory presented in this paper.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Shi Wang, Hendra I. Nurdin, Guofeng Zhang, Matthew R. James The purpose of this paper is to present a network realization theory for a class of mixed quantum–classical linear stochastic systems. Two forms, the standard form and the general form, of this class of linear mixed quantum–classical systems are proposed. Necessary and sufficient conditions for their physical realizability are derived. Based on these physical realizability conditions, a network synthesis theory for this class of linear mixed quantum–classical systems is developed, which clearly exhibits the quantum component, the classical component, and their interface. An example is used to illustrate the theory presented in this paper.
 An analysis of the SPARSEVA estimate for the finite sample data case
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Huong Ha, James S. Welsh, Cristian R. Rojas, Bo Wahlberg In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for a pair of subspaces. We show how this general bound can be applied to a sparse regression problem to obtain an upper bound of the estimation error for the traditional l1 SPARSEVA problem. Numerical results are used to illustrate the effectiveness of the suggested bound.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Huong Ha, James S. Welsh, Cristian R. Rojas, Bo Wahlberg In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for a pair of subspaces. We show how this general bound can be applied to a sparse regression problem to obtain an upper bound of the estimation error for the traditional l1 SPARSEVA problem. Numerical results are used to illustrate the effectiveness of the suggested bound.
 Decentralized cooperative tracking subject to motion constraints
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Lin Wang, Johan Markdahl, Zhixin Liu, Xiaoming Hu This paper addresses the formation control problem, where three agents are tasked with moving an object cooperatively along a desired trajectory while also adjusting its posture to some desired attitudes, i.e. position and attitude tracking. Two decentralized control laws based on locally available information are proposed. The first control law maintains constant interagent distances over time, i.e. the formation of agents moves as a single rigidbody. The second control law relaxes this constraint by only maintaining similarity of the agent formation as a polygon in Euclidean space.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Lin Wang, Johan Markdahl, Zhixin Liu, Xiaoming Hu This paper addresses the formation control problem, where three agents are tasked with moving an object cooperatively along a desired trajectory while also adjusting its posture to some desired attitudes, i.e. position and attitude tracking. Two decentralized control laws based on locally available information are proposed. The first control law maintains constant interagent distances over time, i.e. the formation of agents moves as a single rigidbody. The second control law relaxes this constraint by only maintaining similarity of the agent formation as a polygon in Euclidean space.
 Stochastic Model Predictive Control with adaptive constraint tightening
for nonconservative chance constraints satisfaction Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Diego MuñozCarpintero, Guoqiang Hu, Costas J. Spanos Most stochastic Model Predictive Control (MPC) formulations allow constraint violations via the use of chance constraints, thus increasing control authority and improving performance when compared to their robust MPC counterparts. However, common stochastic MPC methods handle chance constraints conservatively: constraint violations are often smaller than allowed by design, thus limiting the potential improvements in control performance. This is a consequence of enforcing chance constraints overlooking the past behavior of the system and/or of an over tightening of the constraints on the predicted sequences. This work presents a stochastic MPC strategy that uses the observed amount of constraint violations to adaptively scale the tightening parameters, thus eliminating the aforementioned conservativeness. It is proven using Stochastic Approximation that, under suitable conditions, the amount of constraint violations converges in probability when using the proposed method. The effectiveness and benefits of the approach are illustrated by a simulation example.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Diego MuñozCarpintero, Guoqiang Hu, Costas J. Spanos Most stochastic Model Predictive Control (MPC) formulations allow constraint violations via the use of chance constraints, thus increasing control authority and improving performance when compared to their robust MPC counterparts. However, common stochastic MPC methods handle chance constraints conservatively: constraint violations are often smaller than allowed by design, thus limiting the potential improvements in control performance. This is a consequence of enforcing chance constraints overlooking the past behavior of the system and/or of an over tightening of the constraints on the predicted sequences. This work presents a stochastic MPC strategy that uses the observed amount of constraint violations to adaptively scale the tightening parameters, thus eliminating the aforementioned conservativeness. It is proven using Stochastic Approximation that, under suitable conditions, the amount of constraint violations converges in probability when using the proposed method. The effectiveness and benefits of the approach are illustrated by a simulation example.
 Performance boundary output tracking for onedimensional heat equation
with boundary unmatched disturbance Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): FengFei Jin, BaoZhu Guo In this paper, we consider boundary output tracking for a onedimensional heat equation with external disturbance at the opposite end of the bar. First, an unknown input infinitedimensional observer is designed and an estimate of disturbance is obtained from the observer. Second, with reference signal and estimate of disturbance, we design a servo system which has bounded solution given that the reference signal and its derivative are bounded. The output feedback boundary control is then designed by the states of servo system and observer. It is proved that the state of closedloop system tracks the state of the servo system. As a result, the output tracking is included. Finally, some simulation results are presented to illustrate the effectiveness of the proposed scheme.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): FengFei Jin, BaoZhu Guo In this paper, we consider boundary output tracking for a onedimensional heat equation with external disturbance at the opposite end of the bar. First, an unknown input infinitedimensional observer is designed and an estimate of disturbance is obtained from the observer. Second, with reference signal and estimate of disturbance, we design a servo system which has bounded solution given that the reference signal and its derivative are bounded. The output feedback boundary control is then designed by the states of servo system and observer. It is proved that the state of closedloop system tracks the state of the servo system. As a result, the output tracking is included. Finally, some simulation results are presented to illustrate the effectiveness of the proposed scheme.
 Unified stability criteria for slowly timevarying and switched linear
systems Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Xiaobin Gao, Daniel Liberzon, Ji Liu, Tamer Başar This paper presents a unified approach to formulating stability conditions for slowly timevarying linear systems and switched linear systems. The concept of total variation is generalized to the case of matrixvalued functions. Using this generalized concept, a result extending existing stability conditions for slowly timevarying linear systems is derived. As special cases of this result, two sets of stability conditions are derived for switched linear systems, which match known results in the literature. A numerical example is included to further illustrate the application of the main result.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Xiaobin Gao, Daniel Liberzon, Ji Liu, Tamer Başar This paper presents a unified approach to formulating stability conditions for slowly timevarying linear systems and switched linear systems. The concept of total variation is generalized to the case of matrixvalued functions. Using this generalized concept, a result extending existing stability conditions for slowly timevarying linear systems is derived. As special cases of this result, two sets of stability conditions are derived for switched linear systems, which match known results in the literature. A numerical example is included to further illustrate the application of the main result.
 Backstepping stabilization of a linearized ODE–PDE Rijke tube model
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Gustavo Artur de Andrade, Rafael Vazquez, Daniel Juan Pagano The problem of boundary stabilization of thermoacoustic oscillations in the Rijke tube is investigated using the backstepping method; as a first step, this work only considers the fullstate design. This system consists of a vertical tube open at both ends and a heater placed in the lower half of the tube. To study this problem we consider that the mathematical model takes the form of 2 × 2 linear firstorder hyperbolic partial differential equations (PDEs) with a point source term (induced by the Dirac delta distribution) on the right hand side, plus the coupling of an ordinary differential equation (ODE), and control input at one boundary condition. The presence of the Dirac delta distribution implies that the system solution has a discontinuity on a point of the domain, but is continuous everywhere else. We use a coordinate transformation to rewrite the equations into a system of four transport PDEs convecting in opposite directions and to translate the discontinuity to the boundary conditions. Then, a full state feedback backstepping controller is designed to exponentially stabilize the origin. However, the model is nonstrictfeedback making unfeasible the use of standard backstepping designs. This issue is tackled by formulating a wellposed and invertible integral transformation with Volterra and Fredholm terms that maps the Rijke system into a target system with desirable stability properties. An exact piecewisedifferentiable expression for the kernels of this transformation is found, allowing us in turn to derive an explicit feedback control law. Simulation results are presented to illustrate the effectiveness of the proposed control design.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Gustavo Artur de Andrade, Rafael Vazquez, Daniel Juan Pagano The problem of boundary stabilization of thermoacoustic oscillations in the Rijke tube is investigated using the backstepping method; as a first step, this work only considers the fullstate design. This system consists of a vertical tube open at both ends and a heater placed in the lower half of the tube. To study this problem we consider that the mathematical model takes the form of 2 × 2 linear firstorder hyperbolic partial differential equations (PDEs) with a point source term (induced by the Dirac delta distribution) on the right hand side, plus the coupling of an ordinary differential equation (ODE), and control input at one boundary condition. The presence of the Dirac delta distribution implies that the system solution has a discontinuity on a point of the domain, but is continuous everywhere else. We use a coordinate transformation to rewrite the equations into a system of four transport PDEs convecting in opposite directions and to translate the discontinuity to the boundary conditions. Then, a full state feedback backstepping controller is designed to exponentially stabilize the origin. However, the model is nonstrictfeedback making unfeasible the use of standard backstepping designs. This issue is tackled by formulating a wellposed and invertible integral transformation with Volterra and Fredholm terms that maps the Rijke system into a target system with desirable stability properties. An exact piecewisedifferentiable expression for the kernels of this transformation is found, allowing us in turn to derive an explicit feedback control law. Simulation results are presented to illustrate the effectiveness of the proposed control design.
 Robust hierarchical model predictive control of graphbased power flow
systems Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Justin P. Koeln, Andrew G. Alleyne A robust hierarchical model predictive control framework is presented for controlling a linear system of dynamically coupled subsystems. A graphbased modeling framework captures the conservation laws of power flow systems, for which control optimizes the storage and routing of energy to maximize transient and steadystate power throughput. A constructive approach is presented for developing an Nlevel hierarchical controller, which guarantees satisfaction of state and input constraints in the presence of signal and model uncertainty.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Justin P. Koeln, Andrew G. Alleyne A robust hierarchical model predictive control framework is presented for controlling a linear system of dynamically coupled subsystems. A graphbased modeling framework captures the conservation laws of power flow systems, for which control optimizes the storage and routing of energy to maximize transient and steadystate power throughput. A constructive approach is presented for developing an Nlevel hierarchical controller, which guarantees satisfaction of state and input constraints in the presence of signal and model uncertainty.
 Process monitoring using a generalized probabilistic linear latent
variable model Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Rahul Raveendran, Hariprasad Kodamana, Biao Huang This paper defines a generalized probabilistic linear latent variable model (GPLLVM) that under specific restrictions reduces to various probabilistic linear models used for process monitoring. For the defined model, we rigorously derive the monitoring statistics and their respective null distributions. Monitoring statistics of the defined model also reduce to the monitoring statistics of various probabilistic models when restricted with the corresponding conditions. The paper presents insightful equivalence between the classical multivariate techniques for process monitoring and their probabilistic counterparts, which is obtained by restricting the generalized model. We also provide an estimation approach based on the expectation maximization algorithm (EM) for GPLLVM. The results presented in the paper are verified using numerical simulation examples.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Rahul Raveendran, Hariprasad Kodamana, Biao Huang This paper defines a generalized probabilistic linear latent variable model (GPLLVM) that under specific restrictions reduces to various probabilistic linear models used for process monitoring. For the defined model, we rigorously derive the monitoring statistics and their respective null distributions. Monitoring statistics of the defined model also reduce to the monitoring statistics of various probabilistic models when restricted with the corresponding conditions. The paper presents insightful equivalence between the classical multivariate techniques for process monitoring and their probabilistic counterparts, which is obtained by restricting the generalized model. We also provide an estimation approach based on the expectation maximization algorithm (EM) for GPLLVM. The results presented in the paper are verified using numerical simulation examples.
 Periodic eventtriggered sliding mode control
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Abhisek K. Behera, Bijnan Bandyopadhyay, Xinghuo Yu In this paper, we propose the periodic eventtriggering based design of sliding mode control (SMC) for the linear timeinvariant (LTI) systems. In this technique, the triggering instants are generated by a triggering mechanism which is evaluated periodically at those time instants when the state measurements are available. So, the continuous state measurement, as it is usually needed in the continuous eventtriggering strategy, is no longer required in this proposed triggering strategy. The main advantages of this triggering mechanism are: (1) a uniform positive lower bound for the inter event time is guaranteed and (2) this technique is more economical and realistic than its continuous counterpart due to the relaxation of continuous measurements. In this work, we use SMC to design the periodic eventtriggering condition where SMC is designed in such a way that it allows periodic evaluation of triggering rule while guaranteeing the robust performance of the system. Moreover, an upper bound of the sampling period for the periodic measurements is also obtained in this design. Finally, the simulation results are given to demonstrate the design methodology and performance of the system with the proposed eventtriggering strategy.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Abhisek K. Behera, Bijnan Bandyopadhyay, Xinghuo Yu In this paper, we propose the periodic eventtriggering based design of sliding mode control (SMC) for the linear timeinvariant (LTI) systems. In this technique, the triggering instants are generated by a triggering mechanism which is evaluated periodically at those time instants when the state measurements are available. So, the continuous state measurement, as it is usually needed in the continuous eventtriggering strategy, is no longer required in this proposed triggering strategy. The main advantages of this triggering mechanism are: (1) a uniform positive lower bound for the inter event time is guaranteed and (2) this technique is more economical and realistic than its continuous counterpart due to the relaxation of continuous measurements. In this work, we use SMC to design the periodic eventtriggering condition where SMC is designed in such a way that it allows periodic evaluation of triggering rule while guaranteeing the robust performance of the system. Moreover, an upper bound of the sampling period for the periodic measurements is also obtained in this design. Finally, the simulation results are given to demonstrate the design methodology and performance of the system with the proposed eventtriggering strategy.
 From Boolean game to potential game
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Daizhan Cheng, Ting Liu Using semitensor product of matrices, the vector space structure of Boolean games and their some specified subsets are proposed. By resorting to the vector space structure and potential equation, we give an alternative proof for the fact that a symmetric Boolean game is a potential game. The two advantages of this new approach are revealed as follows: (1) It can provide the corresponding potential function; (2) It can be used to explore new potential Boolean games. The corresponding formula is provided to demonstrate the first advantage. As for the second one, the renaming symmetric Boolean games and the weighted symmetric Boolean games are also proved to be potential and weighted potential respectively. Moreover, as a nonsymmetric game, the flipped symmetry Boolean game has been constructed and proved to be potential.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Daizhan Cheng, Ting Liu Using semitensor product of matrices, the vector space structure of Boolean games and their some specified subsets are proposed. By resorting to the vector space structure and potential equation, we give an alternative proof for the fact that a symmetric Boolean game is a potential game. The two advantages of this new approach are revealed as follows: (1) It can provide the corresponding potential function; (2) It can be used to explore new potential Boolean games. The corresponding formula is provided to demonstrate the first advantage. As for the second one, the renaming symmetric Boolean games and the weighted symmetric Boolean games are also proved to be potential and weighted potential respectively. Moreover, as a nonsymmetric game, the flipped symmetry Boolean game has been constructed and proved to be potential.
 General linear forward and backward Stochastic difference equations with
applications Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Juanjuan Xu, Huanshui Zhang, Lihua Xie In this paper, we consider a class of general linear forward and , backward stochastic difference equations (FBSDEs) which are fully coupled. The necessary and sufficient conditions for the existence of a (unique) solution to FBSDEs are given in terms of a Riccati equation. Two kinds of stochastic LQ optimal control problem are then studied as applications. First, we derive the optimal solution to the classic stochastic LQ problem by applying the solution to the associated FBSDEs. Secondly, we study a new type of LQ problem governed by a forward–backward stochastic system (FBSS). By applying the maximum principle and the solution to FBSDEs, an explicit solution is given in terms of a Riccati equation. Finally, by exploring the asymptotic behavior of the Riccati equation, we derive an equivalent condition for the meansquare stabilizability of FBSS.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Juanjuan Xu, Huanshui Zhang, Lihua Xie In this paper, we consider a class of general linear forward and , backward stochastic difference equations (FBSDEs) which are fully coupled. The necessary and sufficient conditions for the existence of a (unique) solution to FBSDEs are given in terms of a Riccati equation. Two kinds of stochastic LQ optimal control problem are then studied as applications. First, we derive the optimal solution to the classic stochastic LQ problem by applying the solution to the associated FBSDEs. Secondly, we study a new type of LQ problem governed by a forward–backward stochastic system (FBSS). By applying the maximum principle and the solution to FBSDEs, an explicit solution is given in terms of a Riccati equation. Finally, by exploring the asymptotic behavior of the Riccati equation, we derive an equivalent condition for the meansquare stabilizability of FBSS.
 Optimal scheduling of multiple sensors over shared channels with packet
transmission constraint Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Shuang Wu, Xiaoqiang Ren, Subhrakanti Dey, Ling Shi In this work, we consider the optimal sensory data scheduling of multiple process. A remote estimator is deployed to monitor S independent linear timeinvariant processes. Each process is measured by a sensor, which is capable of computing a local estimate and sending its local state estimate wrapped up in packets to the remote estimator. The lengths of the packets are different due to different dynamics of each process. Consequently, it takes different time durations for the sensors to send the local estimates. In addition, only a portion of all the sensors are allowed to transmit at each time due to bandwidth limitation. We are interested in minimizing the sum of the average estimation error covariance of each process at the remote estimator under such packet transmission and bandwidth constraints. We formulate the problem as an average cost Markov decision process (MDP) over an infinite horizon. We first study the special case when S=1 and find that the optimal scheduling policy always aims to complete transmitting the current estimate. We also derive a sufficient condition for boundedness of the average remote estimation error. We then study the case for general S. We establish the existence of a deterministic and stationary policy for the optimal scheduling problem. We find that the optimal policy has a consistent property among the sensors and a switching type structure. A stochastic algorithm is designed to utilize the structure of the policy to reduce computation complexity. Numerical examples are provided to illustrate the theoretical results.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Shuang Wu, Xiaoqiang Ren, Subhrakanti Dey, Ling Shi In this work, we consider the optimal sensory data scheduling of multiple process. A remote estimator is deployed to monitor S independent linear timeinvariant processes. Each process is measured by a sensor, which is capable of computing a local estimate and sending its local state estimate wrapped up in packets to the remote estimator. The lengths of the packets are different due to different dynamics of each process. Consequently, it takes different time durations for the sensors to send the local estimates. In addition, only a portion of all the sensors are allowed to transmit at each time due to bandwidth limitation. We are interested in minimizing the sum of the average estimation error covariance of each process at the remote estimator under such packet transmission and bandwidth constraints. We formulate the problem as an average cost Markov decision process (MDP) over an infinite horizon. We first study the special case when S=1 and find that the optimal scheduling policy always aims to complete transmitting the current estimate. We also derive a sufficient condition for boundedness of the average remote estimation error. We then study the case for general S. We establish the existence of a deterministic and stationary policy for the optimal scheduling problem. We find that the optimal policy has a consistent property among the sensors and a switching type structure. A stochastic algorithm is designed to utilize the structure of the policy to reduce computation complexity. Numerical examples are provided to illustrate the theoretical results.
 Fitting jump models
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Alberto Bemporad, Valentina Breschi, Dario Piga, Stephen P. Boyd We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determines the shape of the resulting jump model.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): Alberto Bemporad, Valentina Breschi, Dario Piga, Stephen P. Boyd We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determines the shape of the resulting jump model.
 Asynchronous distributed localization in networks with communication
delays and packet losses Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): XuZhou Huang, YuPing Tian This paper studies the problem of determining sensor locations in a large sensor network using only relative distance (range) measurement. Based on the barycentric coordinate representation, we propose a totally asynchronous distributed algorithm under DILOC framework due to independence of sensor update instants and unreliable networks with communication delays and packet losses. Through modeling the asynchronous algorithm as a linear difference equation with timevarying delays, we prove that the location estimates of sensors are globally convergent to the true coordinates if: (1) time interval between any two consecutive update instants is bounded from below and above, (2) communication delays and successive packet losses between sensors are finite. Simulation examples are provided to demonstrate the effectiveness of the theoretical result.
 Abstract: Publication date: October 2018Source: Automatica, Volume 96Author(s): XuZhou Huang, YuPing Tian This paper studies the problem of determining sensor locations in a large sensor network using only relative distance (range) measurement. Based on the barycentric coordinate representation, we propose a totally asynchronous distributed algorithm under DILOC framework due to independence of sensor update instants and unreliable networks with communication delays and packet losses. Through modeling the asynchronous algorithm as a linear difference equation with timevarying delays, we prove that the location estimates of sensors are globally convergent to the true coordinates if: (1) time interval between any two consecutive update instants is bounded from below and above, (2) communication delays and successive packet losses between sensors are finite. Simulation examples are provided to demonstrate the effectiveness of the theoretical result.
 Robustness, Hansen Lars Peter, Sargent Thomas J. (Eds.). Princeton
University Press (2008), ISBN: 9780691114422 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Tamer Başar
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Tamer Başar
 Mean square consensus of multiagent systems over fading networks with
directed graphs Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Liang Xu, Jianying Zheng, Nan Xiao, Lihua Xie This paper studies the mean square consensus problem of discretetime linear multiagent systems (MASs) over analog fading networks with directed graphs. Compressed inincidence matrix (CIIM), compressed incidence matrix (CIM) and compressed edge Laplacian (CEL) are firstly proposed to facilitate the modeling and consensus analysis. It is then shown that the mean square consensusability is solely determined by the edge state dynamics on a directed spanning tree. As a result, sufficient conditions are provided for mean square consensus over fading networks with directed graphs in terms of fading parameters, the network topology and the agent dynamics. Moreover, the role of network topology on the mean square consensusability is discussed. In the end, simulations are conducted to verify the derived results.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Liang Xu, Jianying Zheng, Nan Xiao, Lihua Xie This paper studies the mean square consensus problem of discretetime linear multiagent systems (MASs) over analog fading networks with directed graphs. Compressed inincidence matrix (CIIM), compressed incidence matrix (CIM) and compressed edge Laplacian (CEL) are firstly proposed to facilitate the modeling and consensus analysis. It is then shown that the mean square consensusability is solely determined by the edge state dynamics on a directed spanning tree. As a result, sufficient conditions are provided for mean square consensus over fading networks with directed graphs in terms of fading parameters, the network topology and the agent dynamics. Moreover, the role of network topology on the mean square consensusability is discussed. In the end, simulations are conducted to verify the derived results.
 Generalized reciprocally convex combination lemmas and its application to
timedelay systems Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Alexandre Seuret, Kun Liu, Frédéric Gouaisbaut Various efficient matrix inequalities have recently been proposed to deal with the stability analysis of linear systems with timevarying delays. This paper provides more insights on the relationship between some of them. We present an equivalent formulation of Moon et al.’s inequality, allowing us to discover strong links not only with the most recent and efficient matrix inequalities such as the reciprocally convex combination lemma and also its relaxed version but also with some previous inequalities such as the approximation inequality introduced in Shao (2009) or freematrixbased inequality. More especially, it is proved that these existing inequalities can be captured as particular cases of Moon et al.’s inequality. Examples show the best tradeoff between the reduction of conservatism and the numerical complexity.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Alexandre Seuret, Kun Liu, Frédéric Gouaisbaut Various efficient matrix inequalities have recently been proposed to deal with the stability analysis of linear systems with timevarying delays. This paper provides more insights on the relationship between some of them. We present an equivalent formulation of Moon et al.’s inequality, allowing us to discover strong links not only with the most recent and efficient matrix inequalities such as the reciprocally convex combination lemma and also its relaxed version but also with some previous inequalities such as the approximation inequality introduced in Shao (2009) or freematrixbased inequality. More especially, it is proved that these existing inequalities can be captured as particular cases of Moon et al.’s inequality. Examples show the best tradeoff between the reduction of conservatism and the numerical complexity.
 An LMIbased approach to distributed model predictive control design for
spatiallyinterconnected systems Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Qin Liu, Hossam Seddik Abbas, Javad Mohammadpour Velni This paper proposes a new framework to distributed model predictive control (MPC) design for linear time and spaceinvariant (LTSI) distributed systems subject to constraints. Given a twodimensional, input–output model that describes the distributed dynamics among the subsystems, it is shown that a nonminimal state space realization leads to numerically tractable linear matrix inequality (LMI) based terminal state feedback controller design. The local online optimization problem is defined at the subsystem level with subsystems exchanging predictions through coupled states and can be solved in parallel at all subsystems noniteratively. Stability and recursive feasibility are guaranteed in the presence of onestep delayed exchanging information among subsystems by imposing consistency constraints and terminal constraints. Attributed to the nonminimal state space realization, input–output properties are preserved in the MPC formulation, and hence no state estimator is needed for the online implementation. Simulation results using a heat equation demonstrate a satisfactory performance of the proposed distributed MPC design compared to centralized MPC schemes.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Qin Liu, Hossam Seddik Abbas, Javad Mohammadpour Velni This paper proposes a new framework to distributed model predictive control (MPC) design for linear time and spaceinvariant (LTSI) distributed systems subject to constraints. Given a twodimensional, input–output model that describes the distributed dynamics among the subsystems, it is shown that a nonminimal state space realization leads to numerically tractable linear matrix inequality (LMI) based terminal state feedback controller design. The local online optimization problem is defined at the subsystem level with subsystems exchanging predictions through coupled states and can be solved in parallel at all subsystems noniteratively. Stability and recursive feasibility are guaranteed in the presence of onestep delayed exchanging information among subsystems by imposing consistency constraints and terminal constraints. Attributed to the nonminimal state space realization, input–output properties are preserved in the MPC formulation, and hence no state estimator is needed for the online implementation. Simulation results using a heat equation demonstrate a satisfactory performance of the proposed distributed MPC design compared to centralized MPC schemes.
 Output feedback control of general linear heterodirectional hyperbolic
ODE–PDE–ODE systems Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Joachim Deutscher, Nicole Gehring, Richard Kern This paper considers the backstepping design of observerbased compensators for general linear heterodirectional hyperbolic ODE–PDE–ODE systems, where the ODEs are coupled to the PDEs at both boundaries and the input appears in an ODE. A state feedback controller is designed by mapping the closedloop system into a stable ODE–PDE–ODE cascade. This is achieved by representing the ODE at the actuated boundary in Byrnes–Isidori normal form. The resulting state feedback is implemented by an observer for a collocated measurement of the PDE state, for which a systematic backstepping approach is presented. The exponential stability of the closedloop system is verified in the ∞norm. It is shown that all design equations can be traced back to kernel equations known from the literature, to simple Volterra integral equations of the second kind and to explicitly solvable boundary value problems. This leads to a systematic approach for the boundary stabilization of the considered class of ODE–PDE–ODE systems by output feedback control. The results of the paper are illustrated by a numerical example.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Joachim Deutscher, Nicole Gehring, Richard Kern This paper considers the backstepping design of observerbased compensators for general linear heterodirectional hyperbolic ODE–PDE–ODE systems, where the ODEs are coupled to the PDEs at both boundaries and the input appears in an ODE. A state feedback controller is designed by mapping the closedloop system into a stable ODE–PDE–ODE cascade. This is achieved by representing the ODE at the actuated boundary in Byrnes–Isidori normal form. The resulting state feedback is implemented by an observer for a collocated measurement of the PDE state, for which a systematic backstepping approach is presented. The exponential stability of the closedloop system is verified in the ∞norm. It is shown that all design equations can be traced back to kernel equations known from the literature, to simple Volterra integral equations of the second kind and to explicitly solvable boundary value problems. This leads to a systematic approach for the boundary stabilization of the considered class of ODE–PDE–ODE systems by output feedback control. The results of the paper are illustrated by a numerical example.

H 2  Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Cecília F. Morais, Jonathan M. Palma, Pedro L.D. Peres, Ricardo C.L.F. Oliveira This paper proposes a new approach based on parameterdependent linear matrix inequality (LMI) conditions associated with a scalar parameter that are sufficient to provide robust H2 and H∞ reducedorder modedependent, partially modedependent or modeindependent filters for discretetime Markov jump linear systems (MJLS) with timeinvariant uncertain transition probabilities. Timeinvariant uncertainties in the state–space matrices of the modes can be handled as well. As main difference with respect to the existing approaches in the literature, the filter matrices are obtained directly from the slack variables introduced in the conditions. Moreover, the proposed conditions become also necessary for a particular choice of the scalar parameter when modedependent fullorder filters are designed for systems without uncertainties. Additionally, for precisely known generalized Bernoulli jump systems (i.e., the case where all the rows of the transition probability matrix are equal), optimal solutions are obtained for both modedependent and modeindependent fullorder filters. Examples (including one motivated by a practical application) are presented to illustrate the proposed approach.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Cecília F. Morais, Jonathan M. Palma, Pedro L.D. Peres, Ricardo C.L.F. Oliveira This paper proposes a new approach based on parameterdependent linear matrix inequality (LMI) conditions associated with a scalar parameter that are sufficient to provide robust H2 and H∞ reducedorder modedependent, partially modedependent or modeindependent filters for discretetime Markov jump linear systems (MJLS) with timeinvariant uncertain transition probabilities. Timeinvariant uncertainties in the state–space matrices of the modes can be handled as well. As main difference with respect to the existing approaches in the literature, the filter matrices are obtained directly from the slack variables introduced in the conditions. Moreover, the proposed conditions become also necessary for a particular choice of the scalar parameter when modedependent fullorder filters are designed for systems without uncertainties. Additionally, for precisely known generalized Bernoulli jump systems (i.e., the case where all the rows of the transition probability matrix are equal), optimal solutions are obtained for both modedependent and modeindependent fullorder filters. Examples (including one motivated by a practical application) are presented to illustrate the proposed approach.
 Useful redundancy in parameter and time delay estimation for
continuoustime models Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Huong Ha, James S. Welsh, Mazen Alamir In this paper we propose an algorithm to estimate the parameters, including time delay, of continuous time systems based on instrumental variable identification methods. To overcome the multiple local minima of the cost function associated with the estimation of a time delay system, we utilize the useful redundancy technique. Specifically, the cost function is filtered through a set of lowpass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the global minimum of the optimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Huong Ha, James S. Welsh, Mazen Alamir In this paper we propose an algorithm to estimate the parameters, including time delay, of continuous time systems based on instrumental variable identification methods. To overcome the multiple local minima of the cost function associated with the estimation of a time delay system, we utilize the useful redundancy technique. Specifically, the cost function is filtered through a set of lowpass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the global minimum of the optimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.
 Coupled boundary interval observer for LPV systems subject to
uncertainties in input, output and parameters Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Stefan Krebs, Matthias Bächle, Sören Hohmann The topic of this publication is the design of interval observers for LPV systems under consideration of parameter, input and output uncertainties that are described by bounded intervals. In the course of the design, also timevarying bounds of the parameter intervals are considered representing the case when parameters are measured with an unknown but bounded measurement error. In this case, an existing approach is extended to handle these parameter uncertainties. The effectiveness of the approach is demonstrated by two numerical examples.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Stefan Krebs, Matthias Bächle, Sören Hohmann The topic of this publication is the design of interval observers for LPV systems under consideration of parameter, input and output uncertainties that are described by bounded intervals. In the course of the design, also timevarying bounds of the parameter intervals are considered representing the case when parameters are measured with an unknown but bounded measurement error. In this case, an existing approach is extended to handle these parameter uncertainties. The effectiveness of the approach is demonstrated by two numerical examples.

H ∞
signals Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Weiming Xiang, James Lam, Panshuo Li In this paper, the stability analysis and H∞ control problems for a class of continuoustime switched systems with a random switching signal are addressed. The dwell time of the switched systems is characterized with a fixed part and a random part. A new stability criterion, which is equivalent to a necessary and sufficient condition developed previously, is established first, and then it is reformulated in terms of linear matrix inequalities. Based on the stability analysis result, L2gain performance analysis and H∞ control problems are studied. Several numerical examples are given to illustrate the effectiveness of our results.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Weiming Xiang, James Lam, Panshuo Li In this paper, the stability analysis and H∞ control problems for a class of continuoustime switched systems with a random switching signal are addressed. The dwell time of the switched systems is characterized with a fixed part and a random part. A new stability criterion, which is equivalent to a necessary and sufficient condition developed previously, is established first, and then it is reformulated in terms of linear matrix inequalities. Based on the stability analysis result, L2gain performance analysis and H∞ control problems are studied. Several numerical examples are given to illustrate the effectiveness of our results.
 Matrix output extension of the tensor network Kalman filter with an
application in MIMO Volterra system identification Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Kim Batselier, Ngai Wong This article extends the tensor network Kalman filter to matrix outputs with an application in recursive identification of discretetime nonlinear multipleinputmultipleoutput (MIMO) Volterra systems. This extension completely supersedes previous work, where only l scalar outputs were considered. The Kalman tensor equations are modified to accommodate for matrix outputs and their implementation using tensor networks is discussed. The MIMO Volterra system identification application requires the conversion of the output model matrix with a rowwise Kronecker product structure into its corresponding tensor network, for which we propose an efficient algorithm. Numerical experiments demonstrate both the efficacy of the proposed matrix conversion algorithm and the improved convergence of the Volterra kernel estimates when using matrix outputs.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Kim Batselier, Ngai Wong This article extends the tensor network Kalman filter to matrix outputs with an application in recursive identification of discretetime nonlinear multipleinputmultipleoutput (MIMO) Volterra systems. This extension completely supersedes previous work, where only l scalar outputs were considered. The Kalman tensor equations are modified to accommodate for matrix outputs and their implementation using tensor networks is discussed. The MIMO Volterra system identification application requires the conversion of the output model matrix with a rowwise Kronecker product structure into its corresponding tensor network, for which we propose an efficient algorithm. Numerical experiments demonstrate both the efficacy of the proposed matrix conversion algorithm and the improved convergence of the Volterra kernel estimates when using matrix outputs.
 Attitude estimation by multiplicative exogenous Kalman filter
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Bård Nagy Stovner, Tor Arne Johansen, Thor I. Fossen, Ingrid Schjølberg This paper presents a novel attitude estimator called the multiplicative exogenous Kalman filter. The estimator inherits the stability properties of a nonlinear observer and the nearoptimal steadystate performance of the linearized Kalman filter for estimation in nonlinear systems. The multiplicative exogenous Kalman filter is derived in detail, and its error dynamics is shown to be globally exponentially stable, which provides guarantees on robustness and transient performance. It is shown in simulations and experiments to yield similar steadystate performance as the multiplicative extended Kalman filter, which is the workhorse for attitude estimation today. The filter assumes biased angular rate measurements and two or more timevarying vector measurements, and it estimates the attitude represented by the quaternion and the angular rate sensor bias.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Bård Nagy Stovner, Tor Arne Johansen, Thor I. Fossen, Ingrid Schjølberg This paper presents a novel attitude estimator called the multiplicative exogenous Kalman filter. The estimator inherits the stability properties of a nonlinear observer and the nearoptimal steadystate performance of the linearized Kalman filter for estimation in nonlinear systems. The multiplicative exogenous Kalman filter is derived in detail, and its error dynamics is shown to be globally exponentially stable, which provides guarantees on robustness and transient performance. It is shown in simulations and experiments to yield similar steadystate performance as the multiplicative extended Kalman filter, which is the workhorse for attitude estimation today. The filter assumes biased angular rate measurements and two or more timevarying vector measurements, and it estimates the attitude represented by the quaternion and the angular rate sensor bias.
 Persistency of excitation and positionsensorless control of permanent
magnet synchronous motors Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Cristiano Maria Verrelli, Patrizio Tomei, Emilio Lorenzani In this brief, the exponential rotor position tracking/regulation problem for positionsensorless (nonsalientpole surface) PMSMs with unknown constant load torque and stator resistance is addressed. The requirement of persistency of excitation conditions involving a nondefinitely zero rotor speed reference is removed, owing to the design of an innovative (speed measurementbased) adaptive observer that relies on a local version of the persistency of excitation lemma and does not involve straightforward adaptations of previous ideas.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Cristiano Maria Verrelli, Patrizio Tomei, Emilio Lorenzani In this brief, the exponential rotor position tracking/regulation problem for positionsensorless (nonsalientpole surface) PMSMs with unknown constant load torque and stator resistance is addressed. The requirement of persistency of excitation conditions involving a nondefinitely zero rotor speed reference is removed, owing to the design of an innovative (speed measurementbased) adaptive observer that relies on a local version of the persistency of excitation lemma and does not involve straightforward adaptations of previous ideas.
 Finitetime and asymptotic left inversion of nonlinear timedelay systems
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Zohra Kader, Gang Zheng, JeanPierre Barbot In this paper we investigate the left invertibility problem for a class of nonlinear timedelay systems. In both cases of time delay systems with and without internal dynamics the invertibility conditions are given. A new approach based on the use of higher order sliding mode observer is developed for finitetime left invertibility and for asymptotic left inversion. Causal and noncausal estimations of the unknown inputs are respectively discussed. The results are illustrated by numerical examples in order to show the efficiency of the method and its limits.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Zohra Kader, Gang Zheng, JeanPierre Barbot In this paper we investigate the left invertibility problem for a class of nonlinear timedelay systems. In both cases of time delay systems with and without internal dynamics the invertibility conditions are given. A new approach based on the use of higher order sliding mode observer is developed for finitetime left invertibility and for asymptotic left inversion. Causal and noncausal estimations of the unknown inputs are respectively discussed. The results are illustrated by numerical examples in order to show the efficiency of the method and its limits.

N coalition+noncooperative+games&rft.title=Automatica&rft.issn=00051098&rft.date=&rft.volume=">Nash equilibrium seeking for N coalition noncooperative games Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Maojiao Ye, Guoqiang Hu, Frank L. Lewis An Ncoalition noncooperative game is formulated in this paper. In the formulated game, there are N interacting coalitions and each of them includes a set of agents. Each coalition acts as a virtual player that aims to minimize its own objective function. This objective function is defined as the sum of the agents’ local objective functions in the coalition and is a function of all the engaged agents’ actions in the game. However, the actual decisionmakers are not the coalitions but the agents therein. That is, the agents within each coalition collaboratively minimize the coalition’s objective function while constituting an entity that serves as a selfinterested player (i.e., the coalition) in the game among the interacting coalitions. A seeking strategy is designed for the agents to find the Nash equilibrium of the Ncoalition noncooperative game. The equilibrium seeking strategy is based on an adaptation of a dynamic average consensus protocol and the gradient play. The dynamic average consensus protocol is leveraged to estimate the averaged gradients of the coalitions’ objective functions. The gradient play is then implemented by utilizing the estimated information to achieve the Nash equilibrium seeking. Convergence results are established by utilizing Lyapunov stability analysis. Numerical examples are given in supportive of the theoretical results.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Maojiao Ye, Guoqiang Hu, Frank L. Lewis An Ncoalition noncooperative game is formulated in this paper. In the formulated game, there are N interacting coalitions and each of them includes a set of agents. Each coalition acts as a virtual player that aims to minimize its own objective function. This objective function is defined as the sum of the agents’ local objective functions in the coalition and is a function of all the engaged agents’ actions in the game. However, the actual decisionmakers are not the coalitions but the agents therein. That is, the agents within each coalition collaboratively minimize the coalition’s objective function while constituting an entity that serves as a selfinterested player (i.e., the coalition) in the game among the interacting coalitions. A seeking strategy is designed for the agents to find the Nash equilibrium of the Ncoalition noncooperative game. The equilibrium seeking strategy is based on an adaptation of a dynamic average consensus protocol and the gradient play. The dynamic average consensus protocol is leveraged to estimate the averaged gradients of the coalitions’ objective functions. The gradient play is then implemented by utilizing the estimated information to achieve the Nash equilibrium seeking. Convergence results are established by utilizing Lyapunov stability analysis. Numerical examples are given in supportive of the theoretical results.
 State and unknown input observers for nonlinear systems with delayed
measurements Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Ankush Chakrabarty, Emilia Fridman, Stanisław H. Żak, Gregery T. Buzzard The use of connected devices or humansintheloop for measuring outputs of dynamical systems inevitably produces timevarying measurement delays. These delays can lead to instability or severe degradation of system performance. In this paper, linear matrix inequalitybased sufficient conditions are proposed for the design of state and unknown input observers based on delayed measurements for a class of nonlinear systems, where the nonlinearities are characterized by incremental multiplier matrices. The proposed observer is guaranteed to perform at specified operational levels in the presence of unknown exogenous inputs acting on the states and measurement outputs. Sufficient conditions are also provided for the estimation of these unknown inputs to a specified degree of accuracy. The potential of the proposed approach is illustrated via estimation of enzyme kinetics.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Ankush Chakrabarty, Emilia Fridman, Stanisław H. Żak, Gregery T. Buzzard The use of connected devices or humansintheloop for measuring outputs of dynamical systems inevitably produces timevarying measurement delays. These delays can lead to instability or severe degradation of system performance. In this paper, linear matrix inequalitybased sufficient conditions are proposed for the design of state and unknown input observers based on delayed measurements for a class of nonlinear systems, where the nonlinearities are characterized by incremental multiplier matrices. The proposed observer is guaranteed to perform at specified operational levels in the presence of unknown exogenous inputs acting on the states and measurement outputs. Sufficient conditions are also provided for the estimation of these unknown inputs to a specified degree of accuracy. The potential of the proposed approach is illustrated via estimation of enzyme kinetics.
 Optimizationfree robust MPC around the terminal region
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Moritz Schulze Darup, Martin Mönnigmann We present a novel dualmode MPC scheme that significantly reduces the computational effort of robust MPC (RMPC). Specifically, we propose a method for the computation of a large set C on which no optimal control problem (OCP) needs to be solved online. The method is motivated by the trivial observation that, for classical MPC, no optimization is required for the states in the terminal set T, because the unconstrained linear–quadratic regulator is optimal there. While this observation cannot be directly transferred to RMPC, we show that suitable sets C exist in the neighborhood of T and state an algorithm for their computation. We stress that the resulting sets C are significantly larger than robust positively invariant sets that are typically exploited in RMPC and on which it is wellknown that no OCP needs to be solved online. The approach is illustrated with three examples for which we observe a reduction of the numerical effort between 22.36% and 95.60%.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Moritz Schulze Darup, Martin Mönnigmann We present a novel dualmode MPC scheme that significantly reduces the computational effort of robust MPC (RMPC). Specifically, we propose a method for the computation of a large set C on which no optimal control problem (OCP) needs to be solved online. The method is motivated by the trivial observation that, for classical MPC, no optimization is required for the states in the terminal set T, because the unconstrained linear–quadratic regulator is optimal there. While this observation cannot be directly transferred to RMPC, we show that suitable sets C exist in the neighborhood of T and state an algorithm for their computation. We stress that the resulting sets C are significantly larger than robust positively invariant sets that are typically exploited in RMPC and on which it is wellknown that no OCP needs to be solved online. The approach is illustrated with three examples for which we observe a reduction of the numerical effort between 22.36% and 95.60%.
 Distributed suboptimal resource allocation over weightbalanced graph via
singular perturbation Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Shu Liang, Xianlin Zeng, Yiguang Hong In this paper, we consider distributed optimization design for resource allocation problems over weightbalanced graphs. With the help of singular perturbation analysis, we propose a simple suboptimal continuoustime optimization algorithm. Moreover, we prove the existence and uniqueness of the algorithm equilibrium, and then show the convergence with an exponential rate. Finally, we verify the suboptimality of the algorithm, which can approach the optimal solution as an adjustable parameter tends to zero.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Shu Liang, Xianlin Zeng, Yiguang Hong In this paper, we consider distributed optimization design for resource allocation problems over weightbalanced graphs. With the help of singular perturbation analysis, we propose a simple suboptimal continuoustime optimization algorithm. Moreover, we prove the existence and uniqueness of the algorithm equilibrium, and then show the convergence with an exponential rate. Finally, we verify the suboptimality of the algorithm, which can approach the optimal solution as an adjustable parameter tends to zero.
 Output feedback Qlearning for discretetime linear zerosum games with
application to the Hinfinity control Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Syed Ali Asad Rizvi, Zongli Lin Approximate dynamic programming techniques usually rely on the feedback of the measurement of the complete state, which is generally not available in practical situations. In this paper, we present an output feedback Qlearning algorithm towards finding the optimal strategies for the discretetime linear quadratic zerosum game, which encompasses the Hinfinity optimal control problem. A new representation of the Qfunction in the output feedback form is derived for the zerosum game problem and the optimal output feedback policies are presented. Then, a Qlearning algorithm is developed that learns the optimal control strategies online without needing any information about the system dynamics, which makes the control design completely modelfree. It is shown that the proposed algorithm converges to the optimal solution obtained by solving the game algebraic Riccati equation (GARE). Unlike the value function based approach used for output feedback, the proposed Qlearning scheme does not require a discounting factor that is generally adopted to mitigate the effect of excitation noise bias. It is known that this discounting factor may compromise the closedloop stability. The proposed method overcomes the excitation noise bias problem without resorting to the discounting factor, and therefore, converges to the nominal GARE solution. As a result, the closedloop stability is preserved. An application to the Hinfinity autopilot controller for the F16 aircraft is demonstrated by simulation.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Syed Ali Asad Rizvi, Zongli Lin Approximate dynamic programming techniques usually rely on the feedback of the measurement of the complete state, which is generally not available in practical situations. In this paper, we present an output feedback Qlearning algorithm towards finding the optimal strategies for the discretetime linear quadratic zerosum game, which encompasses the Hinfinity optimal control problem. A new representation of the Qfunction in the output feedback form is derived for the zerosum game problem and the optimal output feedback policies are presented. Then, a Qlearning algorithm is developed that learns the optimal control strategies online without needing any information about the system dynamics, which makes the control design completely modelfree. It is shown that the proposed algorithm converges to the optimal solution obtained by solving the game algebraic Riccati equation (GARE). Unlike the value function based approach used for output feedback, the proposed Qlearning scheme does not require a discounting factor that is generally adopted to mitigate the effect of excitation noise bias. It is known that this discounting factor may compromise the closedloop stability. The proposed method overcomes the excitation noise bias problem without resorting to the discounting factor, and therefore, converges to the nominal GARE solution. As a result, the closedloop stability is preserved. An application to the Hinfinity autopilot controller for the F16 aircraft is demonstrated by simulation.
 Minimal realizations of nonlinear systems
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Ülle Kotta, Claude H. Moog, Maris Tõnso The nonlinear realization theory is recasted for timevarying singleinput singleoutput nonlinear systems. The concept of realization has been extended to cover also the realizations with order greater than the order of input–output equation. The minimal realization problem is studied. The state realization is said to be minimal if it is either accessible and observable or its state dimension is minimal. In the linear case the two definitions are equivalent, but not for nonlinear timeinvariant systems. It is shown that the two definitions remain equivalent for nonlinear systems under certain technical assumptions. Two alternative methods are presented for finding the minimal realization.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Ülle Kotta, Claude H. Moog, Maris Tõnso The nonlinear realization theory is recasted for timevarying singleinput singleoutput nonlinear systems. The concept of realization has been extended to cover also the realizations with order greater than the order of input–output equation. The minimal realization problem is studied. The state realization is said to be minimal if it is either accessible and observable or its state dimension is minimal. In the linear case the two definitions are equivalent, but not for nonlinear timeinvariant systems. It is shown that the two definitions remain equivalent for nonlinear systems under certain technical assumptions. Two alternative methods are presented for finding the minimal realization.
 Trajectory tracking control of thrustvectoring UAVs
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Davide Invernizzi, Marco Lovera In this paper a geometric approach to the trajectory tracking control of Unmanned Aerial Vehicles (UAVs) with thrust vectoring capabilities is proposed. The control problem is developed within the framework of geometric control theory, yielding a control law that is independent of any parametrization of the configuration space. The proposed design works seamlessly when the thrust vectoring capability is limited, by prioritizing position over attitude tracking. The control law guarantees almostglobal asymptotic tracking of a desired fullpose (attitude and position) trajectory that is compatible with the platform underactuation according to a specific trackability condition. Finally, a numerical example is presented to test the proposed control law on a tiltrotor quadcopter UAV. The generality of the control strategy can be exploited for a broad class of UAVs with thrust vectoring capabilities.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Davide Invernizzi, Marco Lovera In this paper a geometric approach to the trajectory tracking control of Unmanned Aerial Vehicles (UAVs) with thrust vectoring capabilities is proposed. The control problem is developed within the framework of geometric control theory, yielding a control law that is independent of any parametrization of the configuration space. The proposed design works seamlessly when the thrust vectoring capability is limited, by prioritizing position over attitude tracking. The control law guarantees almostglobal asymptotic tracking of a desired fullpose (attitude and position) trajectory that is compatible with the platform underactuation according to a specific trackability condition. Finally, a numerical example is presented to test the proposed control law on a tiltrotor quadcopter UAV. The generality of the control strategy can be exploited for a broad class of UAVs with thrust vectoring capabilities.
 Finitehorizon LQR controller for partiallyobserved Boolean dynamical
systems Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Mahdi Imani, Ulisses M. BragaNeto This paper proposes an approach for finitehorizon control of partiallyobserved Boolean dynamical systems (POBDS) with uncertain continuous control input and infinite observation space. To cope with the partial observability of states, the proposed method first maps the POBDS to an unnormalized belief space. The nonlinear dynamics in this continuous belief space are linearized over a nominal trajectory. Then, the optimal feedback controller is derived, based on the wellknown linear quadratic regulator (LQR), to push the system to follow the nominal trajectory. This nominal trajectory is computed in a planning stage before starting execution, and updated efficiently during execution, whenever the system is found to deviate from the nominal trajectory. We prove that, under mild regularization conditions, the proposed controller approaches the cost of the nominal trajectory as the linearization error approaches zero. The performance of the proposed controller is demonstrated by numerical experiments with a Melanoma gene regulatory network observed through noisy gene expression measurements.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Mahdi Imani, Ulisses M. BragaNeto This paper proposes an approach for finitehorizon control of partiallyobserved Boolean dynamical systems (POBDS) with uncertain continuous control input and infinite observation space. To cope with the partial observability of states, the proposed method first maps the POBDS to an unnormalized belief space. The nonlinear dynamics in this continuous belief space are linearized over a nominal trajectory. Then, the optimal feedback controller is derived, based on the wellknown linear quadratic regulator (LQR), to push the system to follow the nominal trajectory. This nominal trajectory is computed in a planning stage before starting execution, and updated efficiently during execution, whenever the system is found to deviate from the nominal trajectory. We prove that, under mild regularization conditions, the proposed controller approaches the cost of the nominal trajectory as the linearization error approaches zero. The performance of the proposed controller is demonstrated by numerical experiments with a Melanoma gene regulatory network observed through noisy gene expression measurements.
 Adaptive control of uncertain nonlinear systems with quantized input
signal Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Jing Zhou, Changyun Wen, Wei Wang This paper proposes new adaptive controllers for uncertain nonlinear systems in the presence of input quantization. The control signal is quantized by a class of sectorbounded quantizers including the uniform quantizer, the logarithmic quantizer and the hysteresis quantizer. To clearly illustrate our approaches, we will start with a class of singleloop nonlinear systems and then extend the results to multiloop interconnected nonlinear systems. By using backstepping technique, a new adaptive control algorithm is developed by constructing a new compensation method for the effects of the input quantization. A hyperbolic tangent function is introduced in the controller with a new transformation of the control signal. When considering multiloop interconnected systems with interactions, a totally decentralized adaptive control scheme is developed with a new compensation method incorporated for the unknown nonlinear interactions and quantization error. Each local controller, designed simply based on the model of each subsystem by using the adaptive backstepping technique, only employs local information to generate control signals. Unlike some existing control schemes for systems with input quantization, the developed controllers do not require the global Lipschitz condition for the nonlinear functions and also the quantization parameters can be unknown. Besides showing global stability, tracking error performance is also established and can be adjusted by tuning certain design parameters. Simulation results illustrate the effectiveness of our proposed schemes.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Jing Zhou, Changyun Wen, Wei Wang This paper proposes new adaptive controllers for uncertain nonlinear systems in the presence of input quantization. The control signal is quantized by a class of sectorbounded quantizers including the uniform quantizer, the logarithmic quantizer and the hysteresis quantizer. To clearly illustrate our approaches, we will start with a class of singleloop nonlinear systems and then extend the results to multiloop interconnected nonlinear systems. By using backstepping technique, a new adaptive control algorithm is developed by constructing a new compensation method for the effects of the input quantization. A hyperbolic tangent function is introduced in the controller with a new transformation of the control signal. When considering multiloop interconnected systems with interactions, a totally decentralized adaptive control scheme is developed with a new compensation method incorporated for the unknown nonlinear interactions and quantization error. Each local controller, designed simply based on the model of each subsystem by using the adaptive backstepping technique, only employs local information to generate control signals. Unlike some existing control schemes for systems with input quantization, the developed controllers do not require the global Lipschitz condition for the nonlinear functions and also the quantization parameters can be unknown. Besides showing global stability, tracking error performance is also established and can be adjusted by tuning certain design parameters. Simulation results illustrate the effectiveness of our proposed schemes.

G Brownian+motion+with+feedback+control+based+on+discretetime+state+observation&rft.title=Automatica&rft.issn=00051098&rft.date=&rft.volume=">Stabilization of stochastic differential equations driven by G Brownian
motion with feedback control based on discretetime state observation Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Yong Ren, Wensheng Yin, Rathinasamy Sakthivel This paper mainly concerns the stability of the solutions for stochastic differential equations driven by GBrownian motion (GSDEs) via feedback control based on discretetime state observation. More precisely, the discretetime state feedback control is included in the drift coefficient of the GSDEs. By constructing an appropriate GLyapunov function, a set of conditions is obtained for the H∞ stability, asymptotic stability and meansquare exponential stability of the controlled systems. Finally, an example with numerical simulation is presented to illustrate the effectiveness of the proposed control design technique.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Yong Ren, Wensheng Yin, Rathinasamy Sakthivel This paper mainly concerns the stability of the solutions for stochastic differential equations driven by GBrownian motion (GSDEs) via feedback control based on discretetime state observation. More precisely, the discretetime state feedback control is included in the drift coefficient of the GSDEs. By constructing an appropriate GLyapunov function, a set of conditions is obtained for the H∞ stability, asymptotic stability and meansquare exponential stability of the controlled systems. Finally, an example with numerical simulation is presented to illustrate the effectiveness of the proposed control design technique.
 Cooperative robust output regulation of linear uncertain multiple
multivariable systems with performance constraint Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Xinghu Wang, Youfeng Su, Dabo Xu This paper is to pursue a general investigation of cooperative robust output regulation for linear continuoustime multiple multivariable systems with unknown system parameters and unmodeled external disturbances. We show that, under standard minimumphase and relative degree like assumptions, an internal model principle based outputfeedback protocol can be constructed by incorporating suitable dynamic compensators, even when the parametric uncertainties are arbitrarily large in some sense. Moreover, we are able to establish a redesigned protocol by means of adapting the H∞ control method. It assures a desired robustness property for the closedloop system of attenuating external unmodeled disturbances. Hence, our study offers a performanceconstrained robust control solution in a distributed control fashion.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Xinghu Wang, Youfeng Su, Dabo Xu This paper is to pursue a general investigation of cooperative robust output regulation for linear continuoustime multiple multivariable systems with unknown system parameters and unmodeled external disturbances. We show that, under standard minimumphase and relative degree like assumptions, an internal model principle based outputfeedback protocol can be constructed by incorporating suitable dynamic compensators, even when the parametric uncertainties are arbitrarily large in some sense. Moreover, we are able to establish a redesigned protocol by means of adapting the H∞ control method. It assures a desired robustness property for the closedloop system of attenuating external unmodeled disturbances. Hence, our study offers a performanceconstrained robust control solution in a distributed control fashion.
 A linear switching function approach to sliding mode control and
observation of descriptor systems Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Jinghao Li, Qingling Zhang This paper investigates sliding mode control and observation problems for descriptor systems via a linear switching function approach. A generalized regular form and a generalized observer regular form, which are counterparts of the regular form and the observer regular form for normal systems respectively, are first introduced for descriptor systems. Then systematic ways to design the sliding mode controller and the descriptor sliding mode observer for descriptor systems are presented by virtue of linear switching functions. Necessary and sufficient conditions are established to determine the existence of the proposed sliding mode controller and descriptor sliding mode observer. In terms of the proposed sliding mode control and observation method, a descriptor sliding mode observerbased sliding mode controller is also developed for descriptor systems. It shows that under mild assumptions, the associated sliding motion for descriptor systems is of reduced order and the separation principle holds if the amplitude of highorder sliding mode controllers in the control input can be selected appropriately.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Jinghao Li, Qingling Zhang This paper investigates sliding mode control and observation problems for descriptor systems via a linear switching function approach. A generalized regular form and a generalized observer regular form, which are counterparts of the regular form and the observer regular form for normal systems respectively, are first introduced for descriptor systems. Then systematic ways to design the sliding mode controller and the descriptor sliding mode observer for descriptor systems are presented by virtue of linear switching functions. Necessary and sufficient conditions are established to determine the existence of the proposed sliding mode controller and descriptor sliding mode observer. In terms of the proposed sliding mode control and observation method, a descriptor sliding mode observerbased sliding mode controller is also developed for descriptor systems. It shows that under mild assumptions, the associated sliding motion for descriptor systems is of reduced order and the separation principle holds if the amplitude of highorder sliding mode controllers in the control input can be selected appropriately.
 Stabilization of a linear hyperbolic PDE with actuator and sensor dynamics
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Henrik Anfinsen, Ole Morten Aamo We consider a scalar 1D linear hyperbolic partial differential equation (PDE) for which infinitedimensional backstepping controllers have previously been designed based on boundary actuation and sensing, and incorporate first order actuator and sensor dynamics into the design. Two observer designs are proposed, and combined with a statefeedback into outputfeedback control laws which render the origin of the closedloop system exponentially stable with arbitrary convergence rate. The theory is verified in simulations.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Henrik Anfinsen, Ole Morten Aamo We consider a scalar 1D linear hyperbolic partial differential equation (PDE) for which infinitedimensional backstepping controllers have previously been designed based on boundary actuation and sensing, and incorporate first order actuator and sensor dynamics into the design. Two observer designs are proposed, and combined with a statefeedback into outputfeedback control laws which render the origin of the closedloop system exponentially stable with arbitrary convergence rate. The theory is verified in simulations.
 Reduced order LQG control design for port Hamiltonian systems
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Yongxin Wu, Boussad Hamroun, Yann Le Gorrec, Bernhard Maschke The aim of this paper is to propose a reduced order control design method for large scale port Hamiltonian systems. To this end, a structure preserving reduction method and a modified LQG control design are combined to derive a reduced order model suitable for control purposes. We first recall the structure preserving reduction method for port Hamiltonian systems called effort constraint method and characterize the error bound associated to this reduction method. We then give sufficient conditions for nonstandard LQG design which allow to design a passive controller equivalent to the control by interconnection of port Hamiltonian systems. This LQG method allows to define an LQG balanced realization by computing the LQG Gramians, the effortconstraint method is then used to derive a reduced order port Hamiltonian system and to design a reduced order passive LQG controller. Finally, the method is illustrated in simulation on a mass–spring–damper system. The performances of the reduced order controller are compared to the results obtained with a full order passive LQG controller.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Yongxin Wu, Boussad Hamroun, Yann Le Gorrec, Bernhard Maschke The aim of this paper is to propose a reduced order control design method for large scale port Hamiltonian systems. To this end, a structure preserving reduction method and a modified LQG control design are combined to derive a reduced order model suitable for control purposes. We first recall the structure preserving reduction method for port Hamiltonian systems called effort constraint method and characterize the error bound associated to this reduction method. We then give sufficient conditions for nonstandard LQG design which allow to design a passive controller equivalent to the control by interconnection of port Hamiltonian systems. This LQG method allows to define an LQG balanced realization by computing the LQG Gramians, the effortconstraint method is then used to derive a reduced order port Hamiltonian system and to design a reduced order passive LQG controller. Finally, the method is illustrated in simulation on a mass–spring–damper system. The performances of the reduced order controller are compared to the results obtained with a full order passive LQG controller.
 Dissipativitybased boundary control of linear distributed
portHamiltonian systems Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Alessandro Macchelli, Federico Califano The main contribution of this paper is a general synthesis methodology of exponentially stabilising control laws for a class of boundary control systems in portHamiltonian form that are dissipative with respect to a quadratic supply rate, being the total energy the storage function. More precisely, general conditions that a linear regulator has to satisfy to have, at first, a wellposed and, secondly, an exponentially stable closedloop system are presented. The methodology is illustrated with reference to two specific stabilisation scenarios, namely when the (distributed parameter) plant is in impedance or in scattering form. Moreover, it is also shown how these techniques can be employed in the analysis of more general systems that are described by coupled partial and ordinary differential equations. In particular, the repetitive control scheme is studied, and conditions on the (finite dimensional) linear plant to have asymptotic tracking of generic periodic reference signals are determined.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Alessandro Macchelli, Federico Califano The main contribution of this paper is a general synthesis methodology of exponentially stabilising control laws for a class of boundary control systems in portHamiltonian form that are dissipative with respect to a quadratic supply rate, being the total energy the storage function. More precisely, general conditions that a linear regulator has to satisfy to have, at first, a wellposed and, secondly, an exponentially stable closedloop system are presented. The methodology is illustrated with reference to two specific stabilisation scenarios, namely when the (distributed parameter) plant is in impedance or in scattering form. Moreover, it is also shown how these techniques can be employed in the analysis of more general systems that are described by coupled partial and ordinary differential equations. In particular, the repetitive control scheme is studied, and conditions on the (finite dimensional) linear plant to have asymptotic tracking of generic periodic reference signals are determined.
 Inversionbased output tracking and unknown input reconstruction of square
discretetime linear systems Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Esmaeil Naderi, Khashayar Khorasani In this paper, we propose a framework for output tracking control of both minimum phase (MP) and nonminimum phase (NMP) systems as well as systems with transmission zeros on the unit circle. Towards this end, first the problem of unknown state and input reconstruction of nonminimum phase systems is addressed. An unknown input observer (UIO) is designed that accurately reconstructs the minimum phase states of the system. The reconstructed minimum phase states serve as inputs to an FIR filter that is designed for a delayed nonminimum phase state reconstruction. It is shown that a quantified upper bound of the reconstruction error exponentially decreases as the estimation delay is increased. Therefore, an almost perfect state and input reconstruction can be achieved by selecting the delay to be sufficiently large. Our proposed inversion scheme is then applied to solve the outputtracking control problem. Furthermore, we have also proposed a methodology to handle the output tracking problem of systems that have transmission zeros on the unit circle in addition to MP and NMP zeros. Simulation case studies are also presented to demonstrate and illustrate the merits and capabilities of our proposed methodologies.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Esmaeil Naderi, Khashayar Khorasani In this paper, we propose a framework for output tracking control of both minimum phase (MP) and nonminimum phase (NMP) systems as well as systems with transmission zeros on the unit circle. Towards this end, first the problem of unknown state and input reconstruction of nonminimum phase systems is addressed. An unknown input observer (UIO) is designed that accurately reconstructs the minimum phase states of the system. The reconstructed minimum phase states serve as inputs to an FIR filter that is designed for a delayed nonminimum phase state reconstruction. It is shown that a quantified upper bound of the reconstruction error exponentially decreases as the estimation delay is increased. Therefore, an almost perfect state and input reconstruction can be achieved by selecting the delay to be sufficiently large. Our proposed inversion scheme is then applied to solve the outputtracking control problem. Furthermore, we have also proposed a methodology to handle the output tracking problem of systems that have transmission zeros on the unit circle in addition to MP and NMP zeros. Simulation case studies are also presented to demonstrate and illustrate the merits and capabilities of our proposed methodologies.
 On the accuracy of gradient estimation in extremumseeking control using
small perturbations Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Mark Haring, Tor Arne Johansen In many extremumseeking control methods, perturbations are added to the parameter signals to estimate derivatives of the objective function (that is, the steadystate parametertoperformance map) in order to optimize the steadystate performance of the plant using derivativebased algorithms. However, large perturbations are often undesirable or inapplicable due to practical constraints and a high cost of operation. Yet, many extremumseeking control algorithms rely solely on perturbations to estimate all required derivatives. The corresponding derivative estimates, especially the Hessian and higherorder derivatives, may be qualitatively poor if the perturbations are small. In this work, we investigate the use of the nominal parameter signals in addition to the perturbations to improve the accuracy of the gradient estimate. In turn, a more accurate gradient estimate may result in a faster convergence and may allow for a higher tuninggain selection. In addition, we show that, if accurate curvature information of the objective function is available via estimation or a priori knowledge, it may be used to further enhance the accuracy of the gradient estimate.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Mark Haring, Tor Arne Johansen In many extremumseeking control methods, perturbations are added to the parameter signals to estimate derivatives of the objective function (that is, the steadystate parametertoperformance map) in order to optimize the steadystate performance of the plant using derivativebased algorithms. However, large perturbations are often undesirable or inapplicable due to practical constraints and a high cost of operation. Yet, many extremumseeking control algorithms rely solely on perturbations to estimate all required derivatives. The corresponding derivative estimates, especially the Hessian and higherorder derivatives, may be qualitatively poor if the perturbations are small. In this work, we investigate the use of the nominal parameter signals in addition to the perturbations to improve the accuracy of the gradient estimate. In turn, a more accurate gradient estimate may result in a faster convergence and may allow for a higher tuninggain selection. In addition, we show that, if accurate curvature information of the objective function is available via estimation or a priori knowledge, it may be used to further enhance the accuracy of the gradient estimate.
 Distributed sampleddata control of Kuramoto–Sivashinsky equation
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Wen Kang, Emilia Fridman The paper is devoted to distributed sampleddata control of nonlinear PDE system governed by 1D Kuramoto–Sivashinsky equation. It is assumed that N sensors provide sampled in time spatially distributed (either point or averaged) measurements of the state over N sampling spatial intervals. Locally stabilizing sampleddata controllers are designed that are applied through distributed in space shape functions and zeroorder hold devices. Given upper bounds on the sampling intervals in time and in space, sufficient conditions ensuring regional exponential stability of the closedloop system are established in terms of Linear Matrix Inequalities (LMIs) by using the timedelay approach to sampleddata control and Lyapunov–Krasovskii method. As it happened in the case of diffusion equation, the descriptor method appeared to be an efficient tool for the stability analysis of the sampleddata Kuramoto–Sivashinsky equation. An estimate on the domain of attraction is also given. A numerical example demonstrates the efficiency of the results.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Wen Kang, Emilia Fridman The paper is devoted to distributed sampleddata control of nonlinear PDE system governed by 1D Kuramoto–Sivashinsky equation. It is assumed that N sensors provide sampled in time spatially distributed (either point or averaged) measurements of the state over N sampling spatial intervals. Locally stabilizing sampleddata controllers are designed that are applied through distributed in space shape functions and zeroorder hold devices. Given upper bounds on the sampling intervals in time and in space, sufficient conditions ensuring regional exponential stability of the closedloop system are established in terms of Linear Matrix Inequalities (LMIs) by using the timedelay approach to sampleddata control and Lyapunov–Krasovskii method. As it happened in the case of diffusion equation, the descriptor method appeared to be an efficient tool for the stability analysis of the sampleddata Kuramoto–Sivashinsky equation. An estimate on the domain of attraction is also given. A numerical example demonstrates the efficiency of the results.
 Delayrobust stabilization of a hyperbolic PDE–ODE system
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Jean Auriol, Federico BribiescaArgomedo, David Bou Saba, Michael Di Loreto, Florent Di Meglio We detail in this article the development of a delayrobust stabilizing feedback control law for a linear ordinary differential equation coupled with two linear first order hyperbolic equations in the actuation path. The proposed method combines the use of a backstepping approach, required to construct a canceling feedback for the indomain coupling terms of the PDEs, with a second change of variables that reduces the stabilization problem of the PDE–ODE system to that of a timedelay system for which a predictor can be constructed. The proposed controller can be tuned, with some restrictions imposed by the system structure, either by adjusting a reflection coefficient left on the PDE after the backstepping transformation, or by choosing the pole placement on the ODE when constructing the predictor, enabling a tradeoff between convergence rate and delayrobustness. The proposed feedback law is finally proved to be robust to small delays in the actuation.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Jean Auriol, Federico BribiescaArgomedo, David Bou Saba, Michael Di Loreto, Florent Di Meglio We detail in this article the development of a delayrobust stabilizing feedback control law for a linear ordinary differential equation coupled with two linear first order hyperbolic equations in the actuation path. The proposed method combines the use of a backstepping approach, required to construct a canceling feedback for the indomain coupling terms of the PDEs, with a second change of variables that reduces the stabilization problem of the PDE–ODE system to that of a timedelay system for which a predictor can be constructed. The proposed controller can be tuned, with some restrictions imposed by the system structure, either by adjusting a reflection coefficient left on the PDE after the backstepping transformation, or by choosing the pole placement on the ODE when constructing the predictor, enabling a tradeoff between convergence rate and delayrobustness. The proposed feedback law is finally proved to be robust to small delays in the actuation.
 Maximizing the smallest eigenvalue of a symmetric matrix: A submodular
optimization approach Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Andrew Clark, Qiqiang Hou, Linda Bushnell, Radha Poovendran This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input nodes in order to guarantee consensus of networks with negative edges as well as maximizing the convergence rate of distributed systems. We develop a submodular optimization approach to maximizing the smallest eigenvalue by first proving that positivity of the eigenvalues of a submatrix can be characterized using the probability distribution of the quadratic form induced by the submatrix. We then exploit that connection to prove that positivedefiniteness of a submatrix can be expressed as a constraint on a submodular function. We prove that our approach results in polynomialtime algorithms with provable bounds on the size of the submatrix. We also present generalizations to nonsymmetric matrices, alternative sufficient conditions for the smallest eigenvalue to exceed a desired bound that are valid for Laplacian matrices, and a numerical evaluation.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Andrew Clark, Qiqiang Hou, Linda Bushnell, Radha Poovendran This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input nodes in order to guarantee consensus of networks with negative edges as well as maximizing the convergence rate of distributed systems. We develop a submodular optimization approach to maximizing the smallest eigenvalue by first proving that positivity of the eigenvalues of a submatrix can be characterized using the probability distribution of the quadratic form induced by the submatrix. We then exploit that connection to prove that positivedefiniteness of a submatrix can be expressed as a constraint on a submodular function. We prove that our approach results in polynomialtime algorithms with provable bounds on the size of the submatrix. We also present generalizations to nonsymmetric matrices, alternative sufficient conditions for the smallest eigenvalue to exceed a desired bound that are valid for Laplacian matrices, and a numerical evaluation.
 A behavioral approach to inversionbased control
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Alessandro Costalunga, Aurelio Piazzi A new simplified behavior theory is proposed to address inversionbased control for linear, nonminimumphase SISO systems. The chosen space of signals is the set of piecewise C∞functions and input–output pairs (as weak solutions) satisfy a differential–integral equation with additional smoothness requirements. A related key result is the output–input (or inverse) representation of the behavior set that leads to the solution of a general stable inversion problem where polynomially unbounded, noncausal desired outputs are allowed. It is shown that this problem has a solution if and only if the smoothness degree of the desired output is greater than or equal to the system relative degree minus one. When this straightforward condition is satisfied, a closedform expression provides the inverse input. Then, an analysis on preaction and postaction control follows. Two examples are included showing the relevance of output signal design in control applications.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Alessandro Costalunga, Aurelio Piazzi A new simplified behavior theory is proposed to address inversionbased control for linear, nonminimumphase SISO systems. The chosen space of signals is the set of piecewise C∞functions and input–output pairs (as weak solutions) satisfy a differential–integral equation with additional smoothness requirements. A related key result is the output–input (or inverse) representation of the behavior set that leads to the solution of a general stable inversion problem where polynomially unbounded, noncausal desired outputs are allowed. It is shown that this problem has a solution if and only if the smoothness degree of the desired output is greater than or equal to the system relative degree minus one. When this straightforward condition is satisfied, a closedform expression provides the inverse input. Then, an analysis on preaction and postaction control follows. Two examples are included showing the relevance of output signal design in control applications.
 Multiple stopping time POMDPs: Structural results & application in
interactive advertising on social media Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Vikram Krishnamurthy, Anup Aprem, Sujay Bhatt This paper considers a multiple stopping time problem for a Markov chain observed in noise, where a decision maker chooses at most L stopping times to maximize a cumulative objective. We formulate the problem as a Partially Observed Markov Decision Process (POMDP) and derive structural results for the optimal multiple stopping policy. The main results are as follows: (i) The optimal multiple stopping policy is shown to be characterized by threshold curves Γl, for l=1,…,L, in the unit simplex of Bayesian Posteriors. (ii) The stopping sets Sl (defined by the threshold curves Γl) are shown to exhibit the following nested structure Sl−1⊂Sl. (iii) The optimal cumulative reward is shown to be monotone with respect to the copositive ordering of the transition matrix. (iv) A stochastic gradient algorithm is provided for estimating linear threshold policies by exploiting the structural results. These linear threshold policies approximate the threshold curves Γl, and share the monotone structure of the optimal multiple stopping policy. (v) Application of the multiple stopping framework to interactively schedule advertisements in live online social media. It is shown that advertisement scheduling using multiple stopping performs significantly better than currently used methods.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Vikram Krishnamurthy, Anup Aprem, Sujay Bhatt This paper considers a multiple stopping time problem for a Markov chain observed in noise, where a decision maker chooses at most L stopping times to maximize a cumulative objective. We formulate the problem as a Partially Observed Markov Decision Process (POMDP) and derive structural results for the optimal multiple stopping policy. The main results are as follows: (i) The optimal multiple stopping policy is shown to be characterized by threshold curves Γl, for l=1,…,L, in the unit simplex of Bayesian Posteriors. (ii) The stopping sets Sl (defined by the threshold curves Γl) are shown to exhibit the following nested structure Sl−1⊂Sl. (iii) The optimal cumulative reward is shown to be monotone with respect to the copositive ordering of the transition matrix. (iv) A stochastic gradient algorithm is provided for estimating linear threshold policies by exploiting the structural results. These linear threshold policies approximate the threshold curves Γl, and share the monotone structure of the optimal multiple stopping policy. (v) Application of the multiple stopping framework to interactively schedule advertisements in live online social media. It is shown that advertisement scheduling using multiple stopping performs significantly better than currently used methods.
 What information really matters in supervisor reduction'
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Rong Su, W. Murray Wonham To make a supervisor comprehensible to a designer has been a longstanding goal in the supervisory control community. One strategy is to reduce the size of a supervisor to generate a control equivalent version, whose size is optimistically much smaller than the original one so that a user or control designer can easily check whether a designed controller fulfils its objectives and requirements. After the first journal paper on this topic appeared in 1986 by Vaz and Wonham, which relied on the concept of control covers, Su and Wonham proposed in 2004 to use control congruences to ensure computational viability. This work was later adopted in supervisor localization theory, which aims for a control equivalent distributed implementation of a given centralized supervisor. Despite these publications some fundamental questions, which might have been addressed in the first place, have not yet been answered, namely what information is critical to ensure control equivalence, what information is responsible for size reduction, and whether partial observation makes the problem essentially different. In this paper we address these questions by showing that there exists a unified supervisor reduction theory, which is applicable to all feasible supervisors regardless of whether they are under full observation or partial observation. Our theory proposes a preorder (called leanness) over all control equivalent feasible supervisors based on their enabling, disabling and marking information such that, if a supervisor S1 is leaner than another supervisor S2, then the size of the minimal control cover defined over the state set of S1 is no bigger than that of S2.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Rong Su, W. Murray Wonham To make a supervisor comprehensible to a designer has been a longstanding goal in the supervisory control community. One strategy is to reduce the size of a supervisor to generate a control equivalent version, whose size is optimistically much smaller than the original one so that a user or control designer can easily check whether a designed controller fulfils its objectives and requirements. After the first journal paper on this topic appeared in 1986 by Vaz and Wonham, which relied on the concept of control covers, Su and Wonham proposed in 2004 to use control congruences to ensure computational viability. This work was later adopted in supervisor localization theory, which aims for a control equivalent distributed implementation of a given centralized supervisor. Despite these publications some fundamental questions, which might have been addressed in the first place, have not yet been answered, namely what information is critical to ensure control equivalence, what information is responsible for size reduction, and whether partial observation makes the problem essentially different. In this paper we address these questions by showing that there exists a unified supervisor reduction theory, which is applicable to all feasible supervisors regardless of whether they are under full observation or partial observation. Our theory proposes a preorder (called leanness) over all control equivalent feasible supervisors based on their enabling, disabling and marking information such that, if a supervisor S1 is leaner than another supervisor S2, then the size of the minimal control cover defined over the state set of S1 is no bigger than that of S2.
 PDEbased optimization for stochastic mapping and coverage strategies
using robotic ensembles Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Karthik Elamvazhuthi, Hendrik Kuiper, Spring Berman This paper presents a novel partial differential equation (PDE)based framework for controlling an ensemble of robots, which have limited sensing and actuation capabilities and exhibit stochastic behaviors, to perform mapping and coverage tasks. We model the ensemble population dynamics as an advection–diffusion–reaction PDE model and formulate the mapping and coverage tasks as identification and control problems for this model. In the mapping task, robots are deployed over a closed domain to gather data, which is unlocalized and independent of robot identities, for reconstructing the unknown spatial distribution of a region of interest. We frame this task as a convex optimization problem whose solution represents the region as a spatiallydependent coefficient in the PDE model. We then consider a coverage problem in which the robots must perform a desired activity at a programmable probability rate to achieve a target spatial distribution of activity over the reconstructed region of interest. We formulate this task as an optimal control problem in which the PDE model is expressed as a bilinear control system, with the robots’ coverage activity rate and velocity field defined as the control inputs. We validate our approach with simulations of a combined mapping and coverage scenario in two environments with three target coverage distributions.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Karthik Elamvazhuthi, Hendrik Kuiper, Spring Berman This paper presents a novel partial differential equation (PDE)based framework for controlling an ensemble of robots, which have limited sensing and actuation capabilities and exhibit stochastic behaviors, to perform mapping and coverage tasks. We model the ensemble population dynamics as an advection–diffusion–reaction PDE model and formulate the mapping and coverage tasks as identification and control problems for this model. In the mapping task, robots are deployed over a closed domain to gather data, which is unlocalized and independent of robot identities, for reconstructing the unknown spatial distribution of a region of interest. We frame this task as a convex optimization problem whose solution represents the region as a spatiallydependent coefficient in the PDE model. We then consider a coverage problem in which the robots must perform a desired activity at a programmable probability rate to achieve a target spatial distribution of activity over the reconstructed region of interest. We formulate this task as an optimal control problem in which the PDE model is expressed as a bilinear control system, with the robots’ coverage activity rate and velocity field defined as the control inputs. We validate our approach with simulations of a combined mapping and coverage scenario in two environments with three target coverage distributions.
 Retrofit control: Localization of controller design and implementation
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Takayuki Ishizaki, Tomonori Sadamoto, Junichi Imura, Henrik Sandberg, Karl Henrik Johansson In this paper, we propose a retrofit control method for stable network systems. The proposed approach is a control method that, rather than an entire system model, requires a model of the subsystem of interest for controller design. To design the retrofit controller, we use a novel approach based on hierarchical statespace expansion that generates a higherdimensional cascade realization of a given network system. The upstream dynamics of the cascade realization corresponds to an isolated model of the subsystem of interest, which is stabilized by a local controller. The downstream dynamics can be seen as a dynamical model representing the propagation of interference signals among subsystems, the stability of which is equivalent to that of the original system. This cascade structure enables a systematic analysis of both the stability and control performance of the resultant closedloop system. The resultant retrofit controller is formed as a cascade interconnection of the local controller and an output rectifier that rectifies an output signal of the subsystem of interest so as to conform to an output signal of the isolated subsystem model while acquiring complementary signals neglected in the local controller design, such as interconnection signals from neighboring subsystems. Finally, the efficiency of the retrofit control method is demonstrated through numerical examples of power systems control and vehicle platoon control.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Takayuki Ishizaki, Tomonori Sadamoto, Junichi Imura, Henrik Sandberg, Karl Henrik Johansson In this paper, we propose a retrofit control method for stable network systems. The proposed approach is a control method that, rather than an entire system model, requires a model of the subsystem of interest for controller design. To design the retrofit controller, we use a novel approach based on hierarchical statespace expansion that generates a higherdimensional cascade realization of a given network system. The upstream dynamics of the cascade realization corresponds to an isolated model of the subsystem of interest, which is stabilized by a local controller. The downstream dynamics can be seen as a dynamical model representing the propagation of interference signals among subsystems, the stability of which is equivalent to that of the original system. This cascade structure enables a systematic analysis of both the stability and control performance of the resultant closedloop system. The resultant retrofit controller is formed as a cascade interconnection of the local controller and an output rectifier that rectifies an output signal of the subsystem of interest so as to conform to an output signal of the isolated subsystem model while acquiring complementary signals neglected in the local controller design, such as interconnection signals from neighboring subsystems. Finally, the efficiency of the retrofit control method is demonstrated through numerical examples of power systems control and vehicle platoon control.
 State synchronization of multiagent systems via static or adaptive
nonlinear dynamic protocols Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Zhenwei Liu, Meirong Zhang, Ali Saberi, Anton A. Stoorvogel This paper studies state synchronization of homogeneous multiagent systems (MAS) with partialstate coupling. We identify four classes of agents, for which static linear protocol can be designed. They are agents which are squareddown passive, squareddown passifiable via output feedback, squareddown passifiable via input feedforward and squareddown minimumphase with relative degree 1. We find that, for agents which are squareddown passive, the static protocol does not need any network information, as long as the network graph contains a directed spanning tree. For the other three classes of agents, the static protocol needs rough information on the network graph, that is either a lower bound for the real part or an upper bound for the modulus of the nonzero eigenvalues of the Laplacian matrix associated with the network graph. However, when adaptive nonlinear dynamic protocols are utilized, even this rough information about the network can be dispensed with.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Zhenwei Liu, Meirong Zhang, Ali Saberi, Anton A. Stoorvogel This paper studies state synchronization of homogeneous multiagent systems (MAS) with partialstate coupling. We identify four classes of agents, for which static linear protocol can be designed. They are agents which are squareddown passive, squareddown passifiable via output feedback, squareddown passifiable via input feedforward and squareddown minimumphase with relative degree 1. We find that, for agents which are squareddown passive, the static protocol does not need any network information, as long as the network graph contains a directed spanning tree. For the other three classes of agents, the static protocol needs rough information on the network graph, that is either a lower bound for the real part or an upper bound for the modulus of the nonzero eigenvalues of the Laplacian matrix associated with the network graph. However, when adaptive nonlinear dynamic protocols are utilized, even this rough information about the network can be dispensed with.
 Freeendpoint optimal control of inhomogeneous bilinear ensemble systems
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Shuo Wang, JrShin Li Optimal control of bilinear systems has been a wellstudied subject in the areas of mathematical and computational optimal control. However, effective methods for solving emerging optimal control problems involving an ensemble of deterministic or stochastic bilinear systems are underdeveloped. These burgeoning problems arise in diverse applications from quantum control and molecular imaging to neuroscience. In this work, we develop an iterative method to find optimal controls for an inhomogeneous bilinear ensemble system with freeendpoint conditions. The central idea is to represent the bilinear ensemble system at each iteration as a timevarying linear ensemble system, and then solve it in an iterative manner. We analyze convergence of the iterative procedure and discuss optimality of the convergent solutions. The method is directly applicable to solve the same class of optimal control problems involving a stochastic bilinear ensemble system driven by independent additive noise processes. We demonstrate the robustness and applicability of the developed iterative method through practical control designs in neuroscience and quantum control.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Shuo Wang, JrShin Li Optimal control of bilinear systems has been a wellstudied subject in the areas of mathematical and computational optimal control. However, effective methods for solving emerging optimal control problems involving an ensemble of deterministic or stochastic bilinear systems are underdeveloped. These burgeoning problems arise in diverse applications from quantum control and molecular imaging to neuroscience. In this work, we develop an iterative method to find optimal controls for an inhomogeneous bilinear ensemble system with freeendpoint conditions. The central idea is to represent the bilinear ensemble system at each iteration as a timevarying linear ensemble system, and then solve it in an iterative manner. We analyze convergence of the iterative procedure and discuss optimality of the convergent solutions. The method is directly applicable to solve the same class of optimal control problems involving a stochastic bilinear ensemble system driven by independent additive noise processes. We demonstrate the robustness and applicability of the developed iterative method through practical control designs in neuroscience and quantum control.
 Reachability analysis of linear dynamic systems with constant, arbitrary,
and Lipschitz continuous inputs Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Hugo Nestor Villegas Pico, Dionysios C. Aliprantis This paper sets forth a method for reachability analysis of linear dynamic systems in continuous time that can be used to compute timedomain bounds of states and outputs with floatingpoint precision. The focus is on the particular initial conditions and inputs that cause state or output trajectories to attain their extreme values in time. Inputs can be constant, arbitrary, or Lipschitz continuous waveforms. Uncertainties in initial conditions and inputs are modeled using zonotopes. The calculations exploit the definition of zonotopes and the modal information of the linear system dynamics.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Hugo Nestor Villegas Pico, Dionysios C. Aliprantis This paper sets forth a method for reachability analysis of linear dynamic systems in continuous time that can be used to compute timedomain bounds of states and outputs with floatingpoint precision. The focus is on the particular initial conditions and inputs that cause state or output trajectories to attain their extreme values in time. Inputs can be constant, arbitrary, or Lipschitz continuous waveforms. Uncertainties in initial conditions and inputs are modeled using zonotopes. The calculations exploit the definition of zonotopes and the modal information of the linear system dynamics.
 Gridforming control for power converters based on matching of synchronous
machines Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Catalin Arghir, Taouba Jouini, Florian Dörfler We consider the problem of gridforming control of power converters in lowinertia power systems. Starting from an averageswitch threephase power converter model, we draw parallels to a synchronous machine (SM) model and propose a novel converter control strategy which dwells upon the main characteristic of a SM: the presence of an internal rotating magnetic field. In particular, we augment the converter system with a virtual oscillator whose frequency is driven by the DCside voltage measurement and which sets the converter pulsewidthmodulation signal, thereby achieving exact matching between the converter in closedloop and the SM dynamics. We then provide a sufficient condition asserting existence, uniqueness, and global asymptotic stability of a shifted equilibrium, all in a rotating coordinate frame attached to the virtual oscillator angle. By actuating the DCside input of the converter we are able to enforce this condition and provide additional inertia and damping. In this framework, we illustrate strict incremental passivity, droop, and powersharing properties which are compatible with conventional power system operation requirements. We subsequently adopt disturbancedecoupling and droop techniques to design additional control loops that regulate the DCside voltage, as well as ACside frequency and amplitude, while in the end evaluating them with numerical experiments.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Catalin Arghir, Taouba Jouini, Florian Dörfler We consider the problem of gridforming control of power converters in lowinertia power systems. Starting from an averageswitch threephase power converter model, we draw parallels to a synchronous machine (SM) model and propose a novel converter control strategy which dwells upon the main characteristic of a SM: the presence of an internal rotating magnetic field. In particular, we augment the converter system with a virtual oscillator whose frequency is driven by the DCside voltage measurement and which sets the converter pulsewidthmodulation signal, thereby achieving exact matching between the converter in closedloop and the SM dynamics. We then provide a sufficient condition asserting existence, uniqueness, and global asymptotic stability of a shifted equilibrium, all in a rotating coordinate frame attached to the virtual oscillator angle. By actuating the DCside input of the converter we are able to enforce this condition and provide additional inertia and damping. In this framework, we illustrate strict incremental passivity, droop, and powersharing properties which are compatible with conventional power system operation requirements. We subsequently adopt disturbancedecoupling and droop techniques to design additional control loops that regulate the DCside voltage, as well as ACside frequency and amplitude, while in the end evaluating them with numerical experiments.
 On physical realizability of nonlinear quantum stochastic differential
equations Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Muhammad F. Emzir, Matthew J. Woolley, Ian R. Petersen In this article we study physical realizability for a class of nonlinear quantum stochastic differential equations (QSDEs). Physical realizability is a property in which a QSDE corresponds to the dynamics of an open quantum system. We derive a sufficient and necessary condition for a nonlinear QSDE to be physically realizable.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Muhammad F. Emzir, Matthew J. Woolley, Ian R. Petersen In this article we study physical realizability for a class of nonlinear quantum stochastic differential equations (QSDEs). Physical realizability is a property in which a QSDE corresponds to the dynamics of an open quantum system. We derive a sufficient and necessary condition for a nonlinear QSDE to be physically realizable.
 Zonotopebased recursive estimation of the feasible solution set for
linear static systems with additive and multiplicative uncertainties Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Hao Wang, Ilya V. Kolmanovsky, Jing Sun In this paper, we develop two zonotopebased setmembership estimation algorithms for identification of timevarying parameters in linear static models, where both additive and multiplicative uncertainties are treated explicitly. The two recursive algorithms can be differentiated by their ways of processing the data and required computations. The first algorithm, which is referred to as Cone And Zonotope Intersection (CAZI), requires solving linear programming problems at each iteration. The second algorithm, referred to as the Polyhedron And Zonotope Intersection (PAZI), involves linear programming as well as an optimization subject to linear matrix inequalities (LMIs). Both algorithms are capable of providing tight overbounds of the feasible solution set (FSS) in an application to health monitoring of marine engines. Furthermore, PAZI algorithm applied to minibatches of measurement data leads itself to further analysis of the relation between the estimation results at different iterations. In addition, an example of identifying timevarying parameters is also reported.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Hao Wang, Ilya V. Kolmanovsky, Jing Sun In this paper, we develop two zonotopebased setmembership estimation algorithms for identification of timevarying parameters in linear static models, where both additive and multiplicative uncertainties are treated explicitly. The two recursive algorithms can be differentiated by their ways of processing the data and required computations. The first algorithm, which is referred to as Cone And Zonotope Intersection (CAZI), requires solving linear programming problems at each iteration. The second algorithm, referred to as the Polyhedron And Zonotope Intersection (PAZI), involves linear programming as well as an optimization subject to linear matrix inequalities (LMIs). Both algorithms are capable of providing tight overbounds of the feasible solution set (FSS) in an application to health monitoring of marine engines. Furthermore, PAZI algorithm applied to minibatches of measurement data leads itself to further analysis of the relation between the estimation results at different iterations. In addition, an example of identifying timevarying parameters is also reported.
 Gradient extremum seeking for static maps with actuation dynamics governed
by diffusion PDEs Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Jan Feiling, Shumon Koga, Miroslav Krstić, Tiago Roux Oliveira We design and analyze the scalar gradient extremum seeking control feedback for static maps with actuation dynamics governed by diffusion PDEs. Conceptually, a nonmodel based online optimization control scheme is paired with actuation dynamics which occur in chemistry, biology and economics. A learningbased adaptive control approach with known actuation dynamics is considered in this paper. In the design part, we first compensate the actuation dynamics in the dither signals. Secondly, we introduce an averagebased actuation dynamics compensation controller via a backstepping transformation, which is fed by the perturbationbased gradient and Hessian estimates of the static map. The stability analysis of the errordynamics is based on using Lyapunov’s method and applying averaging for infinitedimensional systems to capture the infinitedimensional state of the actuator model. Local exponential convergence to a small neighborhood of the optimal point is proven and illustrated by numerical simulations.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Jan Feiling, Shumon Koga, Miroslav Krstić, Tiago Roux Oliveira We design and analyze the scalar gradient extremum seeking control feedback for static maps with actuation dynamics governed by diffusion PDEs. Conceptually, a nonmodel based online optimization control scheme is paired with actuation dynamics which occur in chemistry, biology and economics. A learningbased adaptive control approach with known actuation dynamics is considered in this paper. In the design part, we first compensate the actuation dynamics in the dither signals. Secondly, we introduce an averagebased actuation dynamics compensation controller via a backstepping transformation, which is fed by the perturbationbased gradient and Hessian estimates of the static map. The stability analysis of the errordynamics is based on using Lyapunov’s method and applying averaging for infinitedimensional systems to capture the infinitedimensional state of the actuator model. Local exponential convergence to a small neighborhood of the optimal point is proven and illustrated by numerical simulations.
 Tensor network subspace identification of polynomial state space models
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Kim Batselier, ChingYun Ko, Ngai Wong This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model is completely written in terms of a tensor network, thus avoiding the curse of dimensionality. We also prove how the block Hankel data matrices in the subspace method can be exactly represented by low rank tensor networks, reducing the computational and storage complexity significantly. The performance and accuracy of our subspace identification algorithm are illustrated by experiments, showing that our tensor network implementation identifies a seventh degree polynomial state space model around 20 times faster than the standard matrix implementation before the latter fails due to insufficient memory. The proposed algorithm is also robust with respect to noise and therefore applicable to practical systems.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Kim Batselier, ChingYun Ko, Ngai Wong This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model is completely written in terms of a tensor network, thus avoiding the curse of dimensionality. We also prove how the block Hankel data matrices in the subspace method can be exactly represented by low rank tensor networks, reducing the computational and storage complexity significantly. The performance and accuracy of our subspace identification algorithm are illustrated by experiments, showing that our tensor network implementation identifies a seventh degree polynomial state space model around 20 times faster than the standard matrix implementation before the latter fails due to insufficient memory. The proposed algorithm is also robust with respect to noise and therefore applicable to practical systems.
 Modal consensus, synchronization and formation control with distributed
endogenous internal models Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Sergio Galeani, Mario Sassano Considering a group of heterogeneous agents communicating over a network, this paper introduces the innovative concept of Distributed Endogenous Internal Model as the key tool for a novel approach to formation control, synchronization and (modal) consensus. The novel strategy yields a dramatic reduction in terms of required communications and computations: in fact, while the usual approach to the mentioned problems entails that each agent is endowed with an internal model of the dynamics specifying the desired collective motion, in the novel approach such dynamics is distributed over the network among the agents, and it is realized in an endogenous fashion, namely by a suitable interconnection among parts of the dynamics already possessed by the agents, through the local cooperation between each agent and its neighbors. To address the cases when the purely endogenous solution is not viable, the related problem of how to minimally augment the dynamics of the overall network of agents in such cases is also studied.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Sergio Galeani, Mario Sassano Considering a group of heterogeneous agents communicating over a network, this paper introduces the innovative concept of Distributed Endogenous Internal Model as the key tool for a novel approach to formation control, synchronization and (modal) consensus. The novel strategy yields a dramatic reduction in terms of required communications and computations: in fact, while the usual approach to the mentioned problems entails that each agent is endowed with an internal model of the dynamics specifying the desired collective motion, in the novel approach such dynamics is distributed over the network among the agents, and it is realized in an endogenous fashion, namely by a suitable interconnection among parts of the dynamics already possessed by the agents, through the local cooperation between each agent and its neighbors. To address the cases when the purely endogenous solution is not viable, the related problem of how to minimally augment the dynamics of the overall network of agents in such cases is also studied.
 Exponential regulation of the anticollocatedly disturbed cage in a wave
PDEmodeled ascending cable elevator Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Ji Wang, ShuXia Tang, Yangjun Pi, Miroslav Krstic In cable elevators, large axial vibrations appear when a cage subject to disturbance is lifted up via a compliant cable. The axial vibration dynamics can be described by a wave partial differential equation (PDE) on a timevarying spatial interval with an unknown boundary disturbance. In this paper, we design an output feedback controller actuating at the boundary anticollocated with the disturbance to regulate the state on the uncontrolled boundary of the wave PDE based on the backstepping idea and the active disturbance rejection control (ADRC) approach. The control law uses the state and disturbance information recovered from the state observer and the disturbance estimator, respectively, which are constructed via limited boundary measurements. The exponential convergence of the state on the uncontrolled boundary and uniform boundedness of all states in the closedloop system are proved by Lyapunov analysis. Effective vibration suppression in the cable elevator with the designed controller is verified via numerical simulation.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Ji Wang, ShuXia Tang, Yangjun Pi, Miroslav Krstic In cable elevators, large axial vibrations appear when a cage subject to disturbance is lifted up via a compliant cable. The axial vibration dynamics can be described by a wave partial differential equation (PDE) on a timevarying spatial interval with an unknown boundary disturbance. In this paper, we design an output feedback controller actuating at the boundary anticollocated with the disturbance to regulate the state on the uncontrolled boundary of the wave PDE based on the backstepping idea and the active disturbance rejection control (ADRC) approach. The control law uses the state and disturbance information recovered from the state observer and the disturbance estimator, respectively, which are constructed via limited boundary measurements. The exponential convergence of the state on the uncontrolled boundary and uniform boundedness of all states in the closedloop system are proved by Lyapunov analysis. Effective vibration suppression in the cable elevator with the designed controller is verified via numerical simulation.
 Measurement and control of nonlinear dynamic systems over the internet
(IoT): Applications in remote control of autonomous vehicles Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Ali Parsa, Alireza Farhadi This paper presents a new technique for almost sure asymptotic state tracking, stability and reference tracking of nonlinear dynamic systems by remote controller over the packet erasure channel, which is an abstract model for transmission via WiFi and the Internet. By implementing a suitable linearization method, a proper encoder and decoder are presented for tracking the state trajectory of nonlinear systems at the end of communication link when the measurements are sent through the packet erasure channel. Then, a controller for reference tracking of the system is designed. In the proposed technique linearization is applied when the error between the states and an estimate of these states at the decoder increases. It is shown that the proposed technique results in almost sure asymptotic reference tracking (and hence stability) over the packet erasure channel. The satisfactory performance of the proposed state trajectory and reference tracking technique is illustrated by computer simulations by applying this technique on the unicycle model, which represents the dynamic of autonomous vehicles.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Ali Parsa, Alireza Farhadi This paper presents a new technique for almost sure asymptotic state tracking, stability and reference tracking of nonlinear dynamic systems by remote controller over the packet erasure channel, which is an abstract model for transmission via WiFi and the Internet. By implementing a suitable linearization method, a proper encoder and decoder are presented for tracking the state trajectory of nonlinear systems at the end of communication link when the measurements are sent through the packet erasure channel. Then, a controller for reference tracking of the system is designed. In the proposed technique linearization is applied when the error between the states and an estimate of these states at the decoder increases. It is shown that the proposed technique results in almost sure asymptotic reference tracking (and hence stability) over the packet erasure channel. The satisfactory performance of the proposed state trajectory and reference tracking technique is illustrated by computer simulations by applying this technique on the unicycle model, which represents the dynamic of autonomous vehicles.
 Dissipativity reinforcement in interconnected systems
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Masaki Inoue, Kengo Urata This paper focuses on the reinforcement of the quantitative performance in interconnected dynamical systems. The following problem is addressed that concerns dissipativity reinforcement via interconnection: Find a class of subsystems and their interconnection rule such that the L2 gain bound of the entire interconnected system is reduced compared with that of each individual subsystem. We assume that each subsystem has a special passivity property that is characterized by two parameters, and has a bounded L2 gain. Then, the feedback connection and the more general interconnection of the subsystems are expressed by the transition of the two parameters inheriting the same passivity property. In addition, the L2 gain bound of the entire interconnected system, estimated with the parameters, is strictly reduced and becomes less than that of each subsystem. Finally, special interconnection rules are considered to show that the scaleexpansion of the interconnected system, i.e., increasing the number of subsystems, gradually reduces the L2 gain bound.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Masaki Inoue, Kengo Urata This paper focuses on the reinforcement of the quantitative performance in interconnected dynamical systems. The following problem is addressed that concerns dissipativity reinforcement via interconnection: Find a class of subsystems and their interconnection rule such that the L2 gain bound of the entire interconnected system is reduced compared with that of each individual subsystem. We assume that each subsystem has a special passivity property that is characterized by two parameters, and has a bounded L2 gain. Then, the feedback connection and the more general interconnection of the subsystems are expressed by the transition of the two parameters inheriting the same passivity property. In addition, the L2 gain bound of the entire interconnected system, estimated with the parameters, is strictly reduced and becomes less than that of each subsystem. Finally, special interconnection rules are considered to show that the scaleexpansion of the interconnected system, i.e., increasing the number of subsystems, gradually reduces the L2 gain bound.
 A distributed Kalman filtering algorithm with fast finitetime convergence
for sensor networks Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Zongze Wu, Minyue Fu, Yong Xu, Renquan Lu This paper proposes a new distributed algorithm for Kalman filtering. It is assumed that a linear discretetime dynamic system is monitored by a network of sensors with some being active and some idle. The goal of distributed state estimation is to devise a distributed algorithm such that each node can independently compute the optimal state estimate by using its local measurements and information exchange with its neighbours. The proposed algorithm applies to acyclic network graphs (i.e., tree graphs) with fast finitetime convergence, but is also applicable to cyclic graphs by combining it with a distributed loop removal algorithm. The proposed algorithm enjoys low complexities, robustness against transmission adversaries and asynchronous implementability. The proposed distributed algorithm also applies to maximum likelihood estimation and weighted leastsquares estimation, as special cases. With simple modifications, the proposed algorithm also applies to an important problem in signal processing called distributed field estimation.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Zongze Wu, Minyue Fu, Yong Xu, Renquan Lu This paper proposes a new distributed algorithm for Kalman filtering. It is assumed that a linear discretetime dynamic system is monitored by a network of sensors with some being active and some idle. The goal of distributed state estimation is to devise a distributed algorithm such that each node can independently compute the optimal state estimate by using its local measurements and information exchange with its neighbours. The proposed algorithm applies to acyclic network graphs (i.e., tree graphs) with fast finitetime convergence, but is also applicable to cyclic graphs by combining it with a distributed loop removal algorithm. The proposed algorithm enjoys low complexities, robustness against transmission adversaries and asynchronous implementability. The proposed distributed algorithm also applies to maximum likelihood estimation and weighted leastsquares estimation, as special cases. With simple modifications, the proposed algorithm also applies to an important problem in signal processing called distributed field estimation.
 Exact recursive updating of state uncertainty sets for linear SISO systems
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Robin Hill, Yousong Luo, Uwe Schwerdtfeger This paper addresses the classical problem of determining the set of possible states of a linear discretetime SISO system subject to bounded disturbances, from measurements corrupted by bounded noise. These socalled uncertainty sets evolve with time as new measurements become available. We present two theorems which give a complete description of the relationship between uncertainty sets at two successive time instants, and this yields an efficient algorithm for recursively updating uncertainty sets. Numerical simulations demonstrate performance improvements over existing exact methods.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Robin Hill, Yousong Luo, Uwe Schwerdtfeger This paper addresses the classical problem of determining the set of possible states of a linear discretetime SISO system subject to bounded disturbances, from measurements corrupted by bounded noise. These socalled uncertainty sets evolve with time as new measurements become available. We present two theorems which give a complete description of the relationship between uncertainty sets at two successive time instants, and this yields an efficient algorithm for recursively updating uncertainty sets. Numerical simulations demonstrate performance improvements over existing exact methods.
 A fundamental control performance limit for a class of positive nonlinear
systems Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Graham C. Goodwin, Diego S. Carrasco, Maria M. Seron, Adrian M. Medioli A fundamental performance limit is derived for a class of positive nonlinear systems. The performance limit describes the achievable output response in the presence of a positive disturbance and subject to a sign constraint on the allowable input. An explicit optimal input is derived which minimises the maximum output response whilst ensuring that the minimum output response does not fall below a prespecified lower bound. The result provides a fundamental performance standard against which all control policies, including closed loop schemes, can be compared. Implications of the result are examined in the context of blood glucose regulation for Type 1 Diabetes.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Graham C. Goodwin, Diego S. Carrasco, Maria M. Seron, Adrian M. Medioli A fundamental performance limit is derived for a class of positive nonlinear systems. The performance limit describes the achievable output response in the presence of a positive disturbance and subject to a sign constraint on the allowable input. An explicit optimal input is derived which minimises the maximum output response whilst ensuring that the minimum output response does not fall below a prespecified lower bound. The result provides a fundamental performance standard against which all control policies, including closed loop schemes, can be compared. Implications of the result are examined in the context of blood glucose regulation for Type 1 Diabetes.
 Stable current sharing and voltage balancing in DC microgrids: A
consensusbased secondary control layer Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Michele Tucci, Lexuan Meng, Josep M. Guerrero, Giancarlo FerrariTrecate In this paper, we propose a secondary consensusbased control layer for current sharing and voltage balancing in DC microGrids (mGs). To this purpose, we assume that Distributed Generation Units (DGUs) are equipped with decentralized primary controllers guaranteeing voltage stability. This goal can be achieved using, for instance, PlugandPlay (PnP) regulators, which allow one to analyze the behavior of the closedloop mG by approximating local primary control loops with either unitary gains or firstorder transfer functions. Besides proving exponential stability, current sharing, and voltage balancing, we describe how to design secondary controllers in a PnP fashion when DGUs are added or removed. Theoretical results are complemented by simulations, using a 7DGUs mG implemented in Simulink/PLECS, and experiments on a 3DGUs mG.
 Abstract: Publication date: September 2018Source: Automatica, Volume 95Author(s): Michele Tucci, Lexuan Meng, Josep M. Guerrero, Giancarlo FerrariTrecate In this paper, we propose a secondary consensusbased control layer for current sharing and voltage balancing in DC microGrids (mGs). To this purpose, we assume that Distributed Generation Units (DGUs) are equipped with decentralized primary controllers guaranteeing voltage stability. This goal can be achieved using, for instance, PlugandPlay (PnP) regulators, which allow one to analyze the behavior of the closedloop mG by approximating local primary control loops with either unitary gains or firstorder transfer functions. Besides proving exponential stability, current sharing, and voltage balancing, we describe how to design secondary controllers in a PnP fashion when DGUs are added or removed. Theoretical results are complemented by simulations, using a 7DGUs mG implemented in Simulink/PLECS, and experiments on a 3DGUs mG.
 Eventtriggered control for robust set stabilization of logical control
networks Abstract: Publication date: Available online 27 June 2018Source: AutomaticaAuthor(s): Yalu Li, Haitao Li, Weiwei Sun This paper addresses the robust set stabilization problem of kvalued logical control networks (KVLCNs) via the algebraic state space representation approach, and proposes an eventtriggered control scheme. Based on the algebraic form of KVLCNs, a necessary and sufficient condition is presented for the robust set stabilization of KVLCNs via timevariant state feedback control. Moreover, the eventtriggered control design problem is formulated, and a sufficient condition is presented to design state feedback eventtriggered controllers for the robust set stabilization of KVLCNs.
 Abstract: Publication date: Available online 27 June 2018Source: AutomaticaAuthor(s): Yalu Li, Haitao Li, Weiwei Sun This paper addresses the robust set stabilization problem of kvalued logical control networks (KVLCNs) via the algebraic state space representation approach, and proposes an eventtriggered control scheme. Based on the algebraic form of KVLCNs, a necessary and sufficient condition is presented for the robust set stabilization of KVLCNs via timevariant state feedback control. Moreover, the eventtriggered control design problem is formulated, and a sufficient condition is presented to design state feedback eventtriggered controllers for the robust set stabilization of KVLCNs.
 On dynamic regressor extension and mixing parameter estimators: Two
Luenberger observers interpretations Abstract: Publication date: Available online 25 June 2018Source: AutomaticaAuthor(s): Romeo Ortega, Laurent Praly, Stanislav Aranovskiy, Bowen Yi, Weidong Zhang Dynamic regressor extension and mixing is a new technique for parameter estimation with guaranteed performance improvement – with respect to classical gradient or leastsquares estimators – that has proven instrumental in the solution of several open problems in system identification and adaptive control. In this brief note we give two interpretations of this parameter estimator in terms of the recent extensions, to the cases of nonlinear systems and observation of linear functionals for timevarying systems, of the classical Luenberger’s state observers.
 Abstract: Publication date: Available online 25 June 2018Source: AutomaticaAuthor(s): Romeo Ortega, Laurent Praly, Stanislav Aranovskiy, Bowen Yi, Weidong Zhang Dynamic regressor extension and mixing is a new technique for parameter estimation with guaranteed performance improvement – with respect to classical gradient or leastsquares estimators – that has proven instrumental in the solution of several open problems in system identification and adaptive control. In this brief note we give two interpretations of this parameter estimator in terms of the recent extensions, to the cases of nonlinear systems and observation of linear functionals for timevarying systems, of the classical Luenberger’s state observers.
 Nonsingular terminal slidingmode control of nonlinear planar systems with
global fixedtime stability guarantees Abstract: Publication date: Available online 23 June 2018Source: AutomaticaAuthor(s): Maria Letizia Corradini, Andrea Cristofaro This paper proposes the use of a novel nonsingular Terminal Sliding surface for the finitetime robust stabilization of second order nonlinear plants with matched uncertainties. Mathematical characteristics of the proposed surface are such that a fixed bound naturally exists for the settling time of the state variable, once the surface has been reached. A simple redesign of the control input able to ensure the feature of fixedtime reaching of the sliding surface will be also presented, and fixedtime stability will be guaranteed by the proposed Terminal Sliding Mode Control design method. A careful simulation study has been performed using a benchmark system taken from the literature.
 Abstract: Publication date: Available online 23 June 2018Source: AutomaticaAuthor(s): Maria Letizia Corradini, Andrea Cristofaro This paper proposes the use of a novel nonsingular Terminal Sliding surface for the finitetime robust stabilization of second order nonlinear plants with matched uncertainties. Mathematical characteristics of the proposed surface are such that a fixed bound naturally exists for the settling time of the state variable, once the surface has been reached. A simple redesign of the control input able to ensure the feature of fixedtime reaching of the sliding surface will be also presented, and fixedtime stability will be guaranteed by the proposed Terminal Sliding Mode Control design method. A careful simulation study has been performed using a benchmark system taken from the literature.

H ∞
systems Abstract: Publication date: Available online 20 June 2018Source: AutomaticaAuthor(s): PoFeng Wu, CheeFai Yung, HeSheng Wang In this paper, we explore the geometric structures of the H∞ central controllers for descriptor systems based on the notions of deflating subspaces for singular matrix pencil. A reduced order H∞ controller is given based on the geometric structures addressed in this paper. The geometric connection between the plant and the H∞ controllers is then studied. A numerical example is provided. In terms of the notions of deflating subspaces, all the results and proofs given are clear and simple.
 Abstract: Publication date: Available online 20 June 2018Source: AutomaticaAuthor(s): PoFeng Wu, CheeFai Yung, HeSheng Wang In this paper, we explore the geometric structures of the H∞ central controllers for descriptor systems based on the notions of deflating subspaces for singular matrix pencil. A reduced order H∞ controller is given based on the geometric structures addressed in this paper. The geometric connection between the plant and the H∞ controllers is then studied. A numerical example is provided. In terms of the notions of deflating subspaces, all the results and proofs given are clear and simple.
 On the stability of reproducing kernel Hilbert spaces of discretetime
impulse responses Abstract: Publication date: Available online 18 June 2018Source: AutomaticaAuthor(s): Tianshi Chen, Gianluigi Pillonetto Reproducing kernel Hilbert spaces (RKHSs) have proved themselves to be key tools for the development of powerful machine learning algorithms, the socalled regularized kernelbased approaches.Recently, they have also inspired the design of new linear system identification techniques able to challenge classical parametric prediction error methods. These facts motivate the study of the RKHS theory within the control community. In this note, we focus on the characterization of stable RKHSs, i.e. RKHSs of functions representing stable impulse responses. Related to this, working in an abstract functional analysis framework, Carmeli et al. (2006) has provided conditions for an RKHS to be contained in the classical Lebesgue spaces ℒp. In particular, we specialize this analysis to the discretetime case with p=1. The necessary and sufficient conditions for the stability of an RKHS are worked out by a quite simple proof, more easily accessible to the control community.
 Abstract: Publication date: Available online 18 June 2018Source: AutomaticaAuthor(s): Tianshi Chen, Gianluigi Pillonetto Reproducing kernel Hilbert spaces (RKHSs) have proved themselves to be key tools for the development of powerful machine learning algorithms, the socalled regularized kernelbased approaches.Recently, they have also inspired the design of new linear system identification techniques able to challenge classical parametric prediction error methods. These facts motivate the study of the RKHS theory within the control community. In this note, we focus on the characterization of stable RKHSs, i.e. RKHSs of functions representing stable impulse responses. Related to this, working in an abstract functional analysis framework, Carmeli et al. (2006) has provided conditions for an RKHS to be contained in the classical Lebesgue spaces ℒp. In particular, we specialize this analysis to the discretetime case with p=1. The necessary and sufficient conditions for the stability of an RKHS are worked out by a quite simple proof, more easily accessible to the control community.
 Eventtriggered control for stochastic nonlinear systems
 Abstract: Publication date: Available online 5 June 2018Source: AutomaticaAuthor(s): YongFeng Gao, XiMing Sun, Changyun Wen, Wei Wang In this work, we investigate the problem of eventtriggered stabilization for a class of stochastic nonlinear systems. An eventtriggered control (ETC) approach is proposed by introducing an additional internal dynamic variable. The presented eventtriggered mechanism (ETM) can guarantee the existence of a positive lower bound on interevent times (or called interexecution times). In addition, the presented technique can ensure the second moment asymptotic stability of the closedloop stochastic nonlinear system.
 Abstract: Publication date: Available online 5 June 2018Source: AutomaticaAuthor(s): YongFeng Gao, XiMing Sun, Changyun Wen, Wei Wang In this work, we investigate the problem of eventtriggered stabilization for a class of stochastic nonlinear systems. An eventtriggered control (ETC) approach is proposed by introducing an additional internal dynamic variable. The presented eventtriggered mechanism (ETM) can guarantee the existence of a positive lower bound on interevent times (or called interexecution times). In addition, the presented technique can ensure the second moment asymptotic stability of the closedloop stochastic nonlinear system.
 A fixedtime convergent algorithm for distributed convex optimization in
multiagent systems Abstract: Publication date: Available online 2 June 2018Source: AutomaticaAuthor(s): Gang Chen, Zhiyong Li This technical paper presents a distributed continuoustime algorithm to solve multiagent optimization problem with the team objective being the sum of all local convex objective functions while subject to an equality constraint. The optimal solutions are achieved within fixed time which is independent of the initial conditions of agents. This advantage makes it possible to offline preassign the settling time according to task requirements. The fixedtime convergence for the proposed algorithm is rigorously proved with the aid of convex optimization and fixedtime Lyapunov theory. Finally, the algorithm is valuated via an example.
 Abstract: Publication date: Available online 2 June 2018Source: AutomaticaAuthor(s): Gang Chen, Zhiyong Li This technical paper presents a distributed continuoustime algorithm to solve multiagent optimization problem with the team objective being the sum of all local convex objective functions while subject to an equality constraint. The optimal solutions are achieved within fixed time which is independent of the initial conditions of agents. This advantage makes it possible to offline preassign the settling time according to task requirements. The fixedtime convergence for the proposed algorithm is rigorously proved with the aid of convex optimization and fixedtime Lyapunov theory. Finally, the algorithm is valuated via an example.
 Stability of bounded subsets of Metzler sparse matrix cones
 Abstract: Publication date: Available online 2 June 2018Source: AutomaticaAuthor(s): Michael McCreesh, Bahman Gharesifard We study the existence of Hurwitz matrices in a class of Metzler sparse matrix cones, where the nonzero entries are constrained to be in a bounded set. In particular, we provide necessary and sufficient conditions for the existence of one or more Hurwitz matrices in this class of sparse matrix spaces, for scenarios with uniform and nonuniform bounds. Several examples illustrate our results.
 Abstract: Publication date: Available online 2 June 2018Source: AutomaticaAuthor(s): Michael McCreesh, Bahman Gharesifard We study the existence of Hurwitz matrices in a class of Metzler sparse matrix cones, where the nonzero entries are constrained to be in a bounded set. In particular, we provide necessary and sufficient conditions for the existence of one or more Hurwitz matrices in this class of sparse matrix spaces, for scenarios with uniform and nonuniform bounds. Several examples illustrate our results.