Authors:Hongyinping Feng; Bao-Zhu Guo Pages: 1 - 10 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Hongyinping Feng, Bao-Zhu Guo In this paper, we propose a new method, by designing an unknown input type state observer, to stabilize an unstable 1-d heat equation with boundary uncertainty and external disturbance. The state observer is designed in terms of a disturbance estimator. A stabilizing state feedback control is designed for the observer by the backstepping transformation, which is an observer based output feedback stabilizing control for the original system. The well-posedness and stability of the closed-loop system are concluded. The numerical simulations show that the proposed scheme is quite effectively. This is a first result on active disturbance rejection control for a PDE with both boundary uncertainty and external disturbance.

Authors:Gang Zheng; Driss Boutat; Haoping Wang Pages: 11 - 17 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Gang Zheng, Driss Boutat, Haoping Wang This paper investigates observer design problem for a large class of nonlinear singular systems with multiple outputs. We first regularize the singular system by injecting the derivative of outputs into the system. Then differential geometric method is applied to transform the regularized system into a simple normal form, for which a Luenberger-like observer is proposed.

Authors:Marco Frego; Enrico Bertolazzi; Francesco Biral; Daniele Fontanelli; Luigi Palopoli Pages: 18 - 28 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Marco Frego, Enrico Bertolazzi, Francesco Biral, Daniele Fontanelli, Luigi Palopoli We consider the problem of finding an optimal manoeuvre that moves a car-like vehicle between two configurations in minimum time. We propose a two phase algorithm in which a path that joins the two points is first found by solving a geometric optimisation problem, and then the optimal manoeuvre is identified considering the system dynamics and its constraints. We make the assumption that the path is composed of a sequence of clothoids. This choice is justified by theoretical arguments, practical examples and by the existence of very efficient geometric algorithms for the computation of a path of this kind. The focus of the paper is on the computation of the optimal manoeuvre, for which we show a semi-analytical solution that can be produced in a few milliseconds on an embedded platform for a path made of one hundred segments. Our method is considerably faster than approaches based on pure numerical solutions, it is capable to detect when the optimal solution exists and, in this case, compute the optimal control. Finally, the method explicitly considers nonlinear dynamics, aerodynamic drag effect and bounds on the longitudinal and on the lateral acceleration.

Authors:Liguo Zhang; Christophe Prieur Pages: 29 - 37 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Liguo Zhang, Christophe Prieur In this paper, we investigate the stochastic stability of linear hyperbolic conservation laws governed by a finite-state Markov chain. Both system matrices and boundary conditions are subject to the Markov switching. The existence and uniqueness of weak solutions are developed for the stochastic hyperbolic initial–boundary value problem. By means of Lyapunov techniques some sufficient conditions are obtained by seeking the balance between the boundary condition and the transition probability of the Markov process. Particularly, boundary feedback control of a stochastic traffic flow model is developed for the freeway transportation system by integrating the on-ramp metering with the speed limit control.

Authors:Zhenhua Wang; Peng Shi; Cheng-Chew Lim Pages: 38 - 45 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Zhenhua Wang, Peng Shi, Cheng-Chew Lim This paper considers H − ∕ H ∞ fault detection observer design in the finite frequency domain for a class of linear parameter-varying (LPV) descriptor systems. We propose a novel fault detection observer with a non-singular structure. To make the residual sensitive to faults and robust against disturbances, we develop a finite frequency H − ∕ H ∞ design method based on a generalized Kalman–Yakubovich–Popov lemma for LPV descriptor systems. Design conditions for the proposed fault detection observer are derived and converted as linear matrix inequalities. Simulation studies are conducted to demonstrate the performance of the proposed method.

Authors:Gian Paolo Incremona; Michele Cucuzzella; Antonella Ferrara Pages: 46 - 52 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Gian Paolo Incremona, Michele Cucuzzella, Antonella Ferrara This paper deals with the design of a Second-Order Sliding Mode (SOSM) control algorithm able to enhance the closed-loop performance depending on the current working conditions. The novelty of the proposed approach is the design of a nonsmooth switching line, based on the quantization of the uncertainties affecting the system. The quantized uncertainty levels allow one to define nested box sets in the auxiliary state space, i.e., the space of the sliding variable and its first time derivative, and select suitable control amplitudes for each set, in order to guarantee the convergence of the sliding variable to the sliding manifold in a finite time. The proposed algorithm is theoretically analyzed, proving the existence of an upperbound of the reaching time to the origin through the considered quantization levels.

Authors:Ahmadreza Jenabzadeh; Behrouz Safarinejadian Pages: 53 - 62 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Ahmadreza Jenabzadeh, Behrouz Safarinejadian This paper considers the distributed state estimation problem for nonlinear stochastic systems over sensor networks. It is assumed that the nonlinear functions are bounded in the pseudo Lipschitz condition. Based on the stochastic Lyapunov stability theory, a distributed consensus filter (DCF) is proposed for both continuous and discrete nonlinear stochastic systems for each node in a sensor network. It will be shown that the estimation errors of the proposed filters are exponentially ultimately bounded in the sense of mean square in terms of linear matrix inequality (LMI). Furthermore, a criterion is presented to optimize the filter gains based on minimizing the upper bound of mean-square error. Numerical examples are used to verify the theoretical results.

Authors:Aleksandr Aravkin; James V. Burke; Lennart Ljung; Aurelie Lozano; Gianluigi Pillonetto Pages: 63 - 86 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Aleksandr Aravkin, James V. Burke, Lennart Ljung, Aurelie Lozano, Gianluigi Pillonetto State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch–Tung–Striebel and Mayne–Fraser algorithms. Such schemes are equivalent to linear algebraic techniques that minimize a convex quadratic objective function with structure induced by the dynamic model. These classical formulations fall short in many important circumstances. For instance, smoothers obtained using quadratic penalties can fail when outliers are present in the data, and cannot track impulsive inputs and abrupt state changes. Motivated by these shortcomings, generalized Kalman smoothing formulations have been proposed in the last few years, replacing quadratic models with more suitable, often nonsmooth, convex functions. In contrast to classical models, these general estimators require use of iterated algorithms, and these have received increased attention from control, signal processing, machine learning, and optimization communities. In this survey we show that the optimization viewpoint provides the control and signal processing community great freedom in the development of novel modeling and inference frameworks for dynamical systems. We discuss general statistical models for dynamic systems, making full use of nonsmooth convex penalties and constraints, and providing links to important models in signal processing and machine learning. We also survey optimization techniques for these formulations, paying close attention to dynamic problem structure. Modeling concepts and algorithms are illustrated with numerical examples.

Authors:Timothy H. Hughes Pages: 87 - 97 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Timothy H. Hughes We present two linked theorems on passivity: the passive behavior theorem, parts 1 and 2. Part 1 provides necessary and sufficient conditions for a general linear system, described by a set of high order differential equations, to be passive. Part 2 extends the positive-real lemma to include uncontrollable and unobservable state-space systems.

Authors:Rachit Mehra; Sumeet G. Satpute; Faruk Kazi; N.M. Singh Pages: 98 - 103 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Rachit Mehra, Sumeet G. Satpute, Faruk Kazi, N.M. Singh The presently established techniques for control of underactuated mechanical systems are dependent on solving partial differential equations (PDEs) arising out of matching conditions. In this brief a novel controller design methodology for (asymptotic) stabilization of nonlinear systems is proposed that obviates the need of solving PDEs to obtain the control laws. The geometry based energy shaping methodology forms the fully constructive procedure for control of underactuated mechanical systems. The control methodology is based on manipulating symmetric structure of the system such that the power flow is established between the controller and unactuated part of the system. The modifications leads to identification of the two new passive outputs which are further utilized for kinetic and potential shaping and the desired controller is obtained using passivity based techniques. The theory is illustrated with two benchmark examples.

Authors:Guangchen Wang; Hua Xiao; Guojing Xing Pages: 104 - 109 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Guangchen Wang, Hua Xiao, Guojing Xing This article is concerned with an optimal control problem derived by mean-field forward–backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are linear with respect to the state and its expectation. The control problem is different from the existing literature concerning optimal control for mean-field stochastic systems, and has more applications in mathematical finance, e.g., asset–liability management problem with recursive utility, systematic risk model. Using a backward separation method with a decomposition technique, two optimality conditions along with two coupled forward–backward optimal filters are derived. Linear–quadratic optimal control problems for mean-field forward–backward stochastic differential equations are studied.

Authors:Marco Caponigro; Benedetto Piccoli; Francesco Rossi; Emmanuel Trélat Pages: 110 - 120 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Marco Caponigro, Benedetto Piccoli, Francesco Rossi, Emmanuel Trélat For control-affine systems with a proper Lyapunov function, the classical Jurdjevic–Quinn procedure (see Jurdjevic and Quinn, 1978) gives a well-known and widely used method for the design of feedback controls that asymptotically stabilize the system to some invariant set. In this procedure, all controls are in general required to be activated, i.e. nonzero, at the same time. In this paper we give sufficient conditions under which this stabilization can be achieved by means of sparse feedback controls, i.e., feedback controls having the smallest possible number of nonzero components. We thus obtain a sparse version of the classical Jurdjevic–Quinn theorem. We propose three different explicit stabilizing control strategies, depending on the method used to handle possible discontinuities arising from the definition of the feedback: a time-varying periodic feedback, a sampled feedback, and a hybrid hysteresis. We illustrate our results by applying them to opinion formation models, thus recovering and generalizing former results for such models.

Authors:Antonio Sala; Manuel Hernández-Mejías; Carlos Ariño Pages: 121 - 128 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Antonio Sala, Manuel Hernández-Mejías, Carlos Ariño This paper discusses predictive control for constrained discrete-time Markov-jump linear systems (MJLS) which jump between a finite set of modes according to a Markov probabilistic transition/observation model, minimising an average cost. Due to the exponential explosion of the number of possible realisations as horizon grows, scenario approaches consider only a subset of them. Prior works cast the problem as a tree-based optimisation one, but enforce stability and feasibility via artificial Lyapunov-related constraints. The proposed approach avoids this route, proposing instead ‘terminal ingredients’ and tree properties (trim-contained, strictly-complete) properly generalising the stability/feasibility ideas in linear and MJLS literature.

Authors:Wu-Hua Chen; Zhen Ruan; Wei Xing Zheng Pages: 129 - 137 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Wu-Hua Chen, Zhen Ruan, Wei Xing Zheng The problems of exponential stability and L 2 -gain for a class of time-delay systems with impulsive effects are studied. The main tool used is the construction of an impulse-time-dependent complete Lyapunov functional. By dividing the impulse interval and delay interval into several segments, the matrix functions of this functional are chosen to be continuous piecewise linear. Moreover, an impulse-time-dependent weighting factor is introduced to coordinate the dynamical behavior of the nondelayed and integral terms of this functional along the trajectories of the system. By applying this functional, delay-dependent sufficient conditions for exponential stability and L 2 -gain are derived in terms of linear matrix inequalities. As by-products, new delay-independent sufficient conditions for the same problems are also derived. The efficiency of the proposed results is illustrated by numerical examples.

Authors:Mondher Farza; Tomas Ménard; Ali Ltaief; Ibtissem Bouraoui; Mohammed M’Saad; Tarak Maatoug Pages: 138 - 146 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Mondher Farza, Tomas Ménard, Ali Ltaief, Ibtissem Bouraoui, Mohammed M’Saad, Tarak Maatoug This paper deals with the design of an Extended High Gain Observer (EHGO) for a large class of Multiple Input Multiple Output (MIMO) non-uniformly observable systems. Indeed, the involved system nonlinearities does not assume the usual triangular structure as it is often the case when a high gain approach is adopted. This structure constraint relaxation is achieved by an appropriate use of the characteristic indices associated to the state components. There are two fundamental features that are worth to be pointed out. Firstly, the gain of the proposed EHGO is provided by an appropriate Riccati Ordinary Differential Equation (ODE). Secondly, the convergence of the observation error is guaranteed under some persistent excitation condition which can be checked on-line. Simulation results are given to illustrate the performance of the proposed EHGO.

Authors:Ruth F. Curtain; Hans Zwart; Orest V. Iftime Pages: 147 - 153 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Ruth F. Curtain, Hans Zwart, Orest V. Iftime Assuming only strong stabilizability, we construct the maximal solution of the algebraic Riccati equation as the strong limit of a Kleinman–Newton sequence of bounded nonnegative operators. As a corollary we obtain a comparison of the solutions of two algebraic Riccati equations associated with different cost functions. We show that the weaker strong stabilizability assumptions are satisfied by partial differential systems with collocated actuators and sensors, so the results have potential applications to numerical approximations of such systems. By means of a counterexample, we illustrate that even if one assumes exponential stabilizability, the Kleinman–Newton construction may provide a solution to the Riccati equation that is not strongly stabilizing.

Authors:Taiga Saito; Akihiko Takahashi Pages: 154 - 165 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Taiga Saito, Akihiko Takahashi This paper investigates the derivatives pricing under the existence of liquidity costs and market impact for the underlying asset in continuous time. First, we formulate the charge for the liquidity costs and the market impact on the derivatives prices through a stochastic control problem that aims to maximize the mark-to-market value of the portfolio less the quadratic variation multiplied by a risk aversion parameter during the hedging period and the liquidation cost at maturity. Then, we obtain the derivatives price by reduction of this charge from the premium in the Bachelier model. Second, we consider a second order semilinear partial differential equation (PDE) of parabolic type associated with the control problem, which is analytically solved or approximated by an asymptotic expansion around a solution to an explicitly solvable nonlinear PDE. Finally, we present the numerical examples of the pricing for a variance option and a European call option, and show comparative static analyses.

Authors:Supratim Ghosh; Justin Ruths; Anders Yeo Pages: 166 - 173 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Supratim Ghosh, Justin Ruths, Anders Yeo In prior work, we established exact graphical conditions for the structural controllability of discrete-time rank-one bilinear systems. Controllability of these systems, with a single-input and rank-one input matrix, involves checking a greatest common divisor condition, which translates to finding a set of walks of coprime lengths in the network of connectivity implied by the state interconnections. Although we established this graphical condition, there was no approach to check for these coprime walks except through brute force matrix products. Here we present a graphical algorithm to guarantee the existence of coprime walks by constructing a cyclic partition of the state graph. This graphical approach provides both computational advantages and additional theoretical insight by identifying an equivalence between the cyclic partition and the existence of controllably invariant subspaces in the state-space.

Authors:Giordano Pola; Elena De Santis; Maria Domenica Di Benedetto; Davide Pezzuti Pages: 174 - 182 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Giordano Pola, Elena De Santis, Maria Domenica Di Benedetto, Davide Pezzuti Motivated by safety-critical applications in cyber–physical systems, in this paper we study the notion of critical observability and design of observers for networks of Finite State Machines (FSMs). Critical observability corresponds to the possibility of detecting if the current state of an FSM is in a given region of interest, called set of critical states. A critical observer detects on-line the occurrence of critical states. When a large-scale network of FSMs is considered, the construction of such an observer is prohibitive because of the large computational effort needed. We propose a decentralized architecture for critical observers of networks of FSMs, where on-line detection of critical states is performed by local critical observers, each associated with an FSM of the network, which do not need to interact. For the efficient design of decentralized critical observers we first extend on-the-fly algorithms traditionally used in the community of formal methods for the verification and control design of FSMs. We then extend to networks of FSMs, bisimulation theory traditionally given in the community of formal methods for single FSMs. The proposed techniques provide a remarkable computational complexity reduction, as discussed throughout the paper and also demonstrated by means of illustrative examples.

Authors:Franco Blanchini; Giulia Giordano Pages: 183 - 191 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Franco Blanchini, Giulia Giordano For a vast class of dynamical networks, including chemical reaction networks (CRNs) with monotonic reaction rates, the existence of a polyhedral Lyapunov function (PLF) implies structural (i.e., parameter-free) local stability. Global structural stability is ensured under the additional assumption that each of the variables (chemical species concentrations in CRNs) is subject to a spontaneous infinitesimal dissipation. This paper solves the open problem of global structural stability in the absence of the infinitesimal dissipation, showing that the existence of a PLF structurally ensures global convergence if and only if the system Jacobian passes a structural non-singularity test. It is also shown that, if the Jacobian is structurally non-singular, under positivity assumptions for the system partial derivatives, the existence of an equilibrium is guaranteed. For systems subject to positivity constraints, it is shown that, if the system admits a PLF, under structural non-singularity assumptions, global convergence within the positive orthant is structurally ensured, while the existence of an equilibrium can be proven by means of a linear programming test and the computation of a piecewise-linear-in-rate Lyapunov function.

Authors:Christoforos Keroglou; Christoforos N. Hadjicostis Pages: 192 - 198 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Christoforos Keroglou, Christoforos N. Hadjicostis In this paper we analyze state estimation in stochastic discrete event systems (SDES) that can be modeled as probabilistic finite automata (PFAs). For a given PFA, we obtain the necessary and sufficient conditions that guarantee exact state estimation, at least asymptotically, with increasing certainty as more information is acquired from observing the behavior of the given PFA, by defining the notion of AA-detectability, and providing necessary and sufficient conditions that can be used to verify it. The characterization and analysis of AA-detectability is transformed to a problem of classification between two (or more) PFAs, which capture the recurrent behavior of an underlying Markov process that is obtained by ignoring output behavior and focusing on state transitions in the given PFA. Our approach combines techniques used in classification between two (or more) PFAs with state estimation methods used in logical discrete event systems (DES). We prove that the proposed verification of AA-detectability is of polynomial complexity with respect to the size of the state space of the given PFA.

Authors:Tao Liu; Ming Cao; Claudio De Persis; Julien M. Hendrickx Pages: 199 - 204 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Tao Liu, Ming Cao, Claudio De Persis, Julien M. Hendrickx This paper studies synchronization of dynamical networks with event-based communication. Firstly, two estimators are introduced into each node, one to estimate its own state, and the other to estimate the average state of its neighbours. Then, with these two estimators, a distributed event-triggering rule (ETR) with a dwell time is designed such that the network achieves synchronization asymptotically with no Zeno behaviours. The designed ETR only depends on the information that each node can obtain, and thus can be implemented in a decentralized way.

Authors:Mingming Liu; Fabian Wirth; Martin Corless; Robert Shorten Pages: 205 - 211 Abstract: Publication date: December 2017 Source:Automatica, Volume 86 Author(s): Mingming Liu, Fabian Wirth, Martin Corless, Robert Shorten We consider a class of consensus systems driven by a nonlinear input. Such systems arise in a class of Internet of Things (IOT) applications. Our objective in this paper is to determine conditions under which a certain partially distributed system converges to a Lur’e-like scalar system, and to provide a rigorous proof of its stability. Conditions are derived for the non-uniform convergence and stability of such a system and an example is given of a speed advisory system where such a system arises.

Authors:Weiming Xiang; James Lam; Jun Shen Pages: 1 - 8 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Weiming Xiang, James Lam, Jun Shen This paper deals with the problems of stability analysis and L 1 -gain characterization for continuous-time switched systems consisting of positive subsystems. With the aid of a discretized copositive Lyapunov function, a sufficient condition ensuring the asymptotic stability of continuous-time switched positive systems under dwell-time constraint is obtained, which can be checked via linear programming. Furthermore, the conservatism of the proposed approach is studied and the result with least conservatism in the framework of discretized copositive Lyapunov function is obtained. The result is then extended to L 1 -gain characterization for switched positive systems. With a prescribed dwell time, an unweighted L 1 -gain can be computed via solving a linear programming problem. A numerical example and a practical traffic example are given to illustrate our results.

Authors:Wei Liu; Peng Shi; Jeng-Shyang Pan Pages: 9 - 21 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Wei Liu, Peng Shi, Jeng-Shyang Pan The state estimation problem for discrete-time Markov jump linear systems corrupted by time-correlated and mode-dependent measurement noise is considered where the time-correlated and mode-dependent measurement noise is described via a discrete-time stochastic system with Markov parameter and Kronecker delta function. By defining the measurement noise in this manner, both time-correlation and periodic step change caused by the change of system environment or structure can be embodied in the measurement noise. A novel “distributed measurement differencing method” is applied to the problem of state estimation under consideration so that two algorithms are obtained using some results presented in this paper. The first algorithm is optimal in the sense of minimum mean-square error, which can exactly compute the minimum mean-square error estimate of system state. The second algorithm is suboptimal and the suboptimality of the algorithm is caused by using some Gaussian hypotheses. The two proposed algorithms are recursive and the proposed suboptimal algorithm has a time-independent complexity. The performance of the proposed suboptimal algorithm is illustrated using computer simulations.

Authors:Thomas Holding; Ioannis Lestas Pages: 22 - 33 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Thomas Holding, Ioannis Lestas We consider the problem of resource allocation in a decentralised market where users and suppliers trade for a single commodity. Due to the lack of strict concavity, convergence to the optimal solution by means of classical gradient type dynamics for the prices and demands, is not guaranteed. In the paper we explicitly characterise in this case the asymptotic behaviour of trajectories and provide an exact characterisation of the limiting oscillatory solutions. Methods of modifying the dynamics are also given, such that convergence to an optimal solution is guaranteed, without requiring additional information exchange among the users.

Authors:Joachim Deutscher Pages: 34 - 42 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Joachim Deutscher This article presents a backstepping solution to the output regulation problem for general linear heterodirectional hyperbolic systems with spatially-varying coefficients. The disturbances can act at both boundaries, distributed in-domain or at the output to be controlled. The latter is defined at a boundary, distributed or pointwise in-domain and has not to be available for measurement. By utilizing backstepping coordinates it is shown that all design equations are explicitly solvable. This allows a simple determination of a state feedback regulator, that is implemented by a reference and a disturbance observer. Furthermore, an easy evaluation of the existence conditions for the resulting output feedback regulator is possible in terms of the plant transfer behaviour. In order to facilitate the parameterization of the regulator, the resulting closed-loop dynamics is directly related to the design parameters. The proposed backstepping-based design of the output feedback regulator is demonstrated for an unstable heterodirectional 4 × 4 hyperbolic system.

Authors:Xiaodong Xu; Stevan Dubljevic Pages: 43 - 52 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Xiaodong Xu, Stevan Dubljevic This manuscript addresses the output regulation problem for a class of scalar boundary controlled first-order hyperbolic partial integro-differential equation (PIDE) systems with Fredholm integrals. In particular, with the advantage of the backstepping approach, simple structure systems can be obtained such that regulator equations for the state feedback regulator design are analyzed and solved in backstepping coordinates. Moreover, the finite time output regulation is achieved. In the observer-based output feedback regulator design, it is not necessary that the outputs to be controlled belong to the available output measurements and these outputs can be distributed, point-wise and/or boundary in nature, while the boundary placed measurements are used for regulator design. For the observer gains design, a transformation of the ODE–PDE system into an ODE–PDE cascade is considered. It is also shown that the separation principle holds for the output feedback regulator design and the exponential output regulation is realized for the resulting stable closed-loop system. Finally, the output regulation results are illustrated with two numerical simulations: a Korteweg–de Vries-like equation and a PDE–ODE interconnected system.

Authors:Huai-Ning Wu; Huan-Yu Zhu Pages: 53 - 60 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Huai-Ning Wu, Huan-Yu Zhu This paper studies the guaranteed cost fuzzy state observer (GCFSO) design via pointwise measurement sensors for a class of distributed parameter systems described by semilinear parabolic partial differential equations (PDEs). Initially, a Takagi–Sugeno (T–S) fuzzy model is employed to accurately represent the original PDE system in a local region. Then, based on the T–S fuzzy model, a fuzzy state observer is constructed for the state estimation. By augmenting the state estimation error system with the fuzzy PDE system and utilizing Lyapunov technique and Wirtinger’s inequality, a fuzzy state observer design with a guaranteed cost is developed in terms of linear matrix inequalities (LMIs). The resulting fuzzy observer can exponentially stabilize the augmented system while providing an upper bound on the cost function of state estimation error. Moreover, a suboptimal GCFSO design problem is also addressed to make the upper bound as small as possible. Finally, the numerical simulation results on two examples demonstrate the effectiveness of the proposed method.

Authors:Hector Ramirez; Hans Zwart; Yann Le Gorrec Pages: 61 - 69 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Hector Ramirez, Hans Zwart, Yann Le Gorrec The conditions for existence of solutions and stability, asymptotic and exponential, of a large class of boundary controlled systems on a 1D spatial domain subject to nonlinear dynamic boundary actuation are given. The consideration of such class of control systems is motivated by the use of actuators and sensors with nonlinear behavior in many engineering applications. These nonlinearities are usually associated to large deformations or the use of smart materials such as piezo actuators and memory shape alloys. Including them in the controller model results in passive dynamic controllers with nonlinear potential energy function and/or nonlinear damping forces. First it is shown that under very natural assumptions the solutions of the partial differential equation with the nonlinear dynamic boundary conditions exist globally. Secondly, when energy dissipation is present in the controller, then it globally asymptotically stabilizes the partial differential equation. Finally, it is shown that assuming some additional conditions on the interconnection and on the passivity properties of the controller (consistent with physical applications) global exponential stability of the closed-loop system is achieved.

Authors:João C.C. Henriques; João M. Lemos; Luís Eça; Luís M.C. Gato; António F.O. Falcão Pages: 70 - 82 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): João C.C. Henriques, João M. Lemos, Luís Eça, Luís M.C. Gato, António F.O. Falcão A high-order Discontinuous Galerkin (DG) finite element time-stepping method is applied for the numerical solution of optimal control problems within the framework of Pontryagin’s Maximum Principle. The method constitutes an efficient and versatile alternative to the well-known Pseudospectral (PS) methods. The two main advantages of DG in comparison with the PS methods are: the local nature of the piecewise polynomial solution and the straightforward implementation of element-wise mesh and polynomial refinement if required. Two types of non-linear optimal control problems were analysed: continuous and bang–bang time-solutions. In the case of bang–bang optimal control problems, anh-refinement strategy was developed to achieve agreement between the observed and the formal order of accuracy. The paper also deals with sub-optimal control problems where: (i) time-step is fixed and non-infinitesimal; (ii) the control has two modes (on/off); (iii) the control command is only applied at the beginning of each time-step; and iv) the number of switching instants is large and not known a priori.

Authors:Chun-Hua Xie; Guang-Hong Yang Pages: 83 - 90 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Chun-Hua Xie, Guang-Hong Yang This paper investigates the decentralized adaptive fault-tolerant control problem for a class of uncertain large-scale interconnected systems with disturbances and actuator faults including stuck, outage and loss of effectiveness. It is assumed that the upper bounds of the disturbances and stuck faults are unknown. The considered disturbances and unknown interconnections contain matched and mismatched parts. A decentralized adaptive control scheme with backstepping method is developed. Then, according to the information from the adaptive mechanism, the effects of both the actuator faults and the matched parts of disturbances and interconnections can be eliminated completely. Furthermore, cyclic-small-gain technique is introduced to address the mismatched interconnections such that the resulting closed-loop system is asymptotically stable with disturbance attenuation level γ . Compared with the existing results, disturbance rejection property can be guaranteed for each subsystem. Finally, a simulation example of a large-scale power system is provided to show the effectiveness of the proposed approach.

Authors:Shunyi Zhao; Biao Huang; Yuriy S. Shmaliy Pages: 91 - 99 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Shunyi Zhao, Biao Huang, Yuriy S. Shmaliy The finite impulse response (FIR) filter and infinite impulse response filter including the Kalman filter (KF) are generally considered as two different types of state estimation methods. In this paper, the sequential Bayesian philosophy is extended to a filter design using a fixed amount of most recent measurements, with the aim of exploiting the FIR structure and unifying some basic FIR filters with the KF. Specifically, the conditional mean and covariance of the posterior probability density functions are first derived to show the FIR counterpart of the KF. To remove the dependence on initial states, the corresponding likelihood is further maximized and realized iteratively. It shows that the maximum likelihood modification unifies the existing unbiased FIR filters by tuning a weighting matrix. Moreover, it converges to the Kalman estimate with the increase of horizon length, and can thus be considered as a link between the FIR filtering and the KF. Several important properties including stability and robustness against errors of noise statistics are illustrated. Finally, a moving target tracking example and an experiment with a three degrees-of-freedom helicopter system are introduced to demonstrate effectiveness.

Authors:Xudong Chen; Mohamed-Ali Belabbas; Tamer Başar Pages: 100 - 112 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Xudong Chen, Mohamed-Ali Belabbas, Tamer Başar We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements. We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the estimation is bounded above, and that each sample requires the same amount of communication. Our goal is then to find an optimal allocation of the capacity to the sensors so that the time-averaged estimation error is minimized. We show that when the total available channel capacity is large, this resource allocation problem can be recast as a strictly convex optimization problem, and hence there exists a unique optimal allocation of the capacity. We further investigate how this optimal allocation varies as the available capacity increases. In particular, we show that if the coupling among the subsystems is weak, then the sampling rate allocated to each sensor is nondecreasing in the total sampling rate, and is strictly increasing if and only if the total sampling rate exceeds a certain threshold.

Authors:Nicolas Gillis; Punit Sharma Pages: 113 - 121 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Nicolas Gillis, Punit Sharma In this paper, we consider the problem of computing the nearest stable matrix to an unstable one. We propose new algorithms to solve this problem based on a reformulation using linear dissipative Hamiltonian systems: we show that a matrix A is stable if and only if it can be written as A = ( J − R ) Q , where J = − J T , R ⪰ 0 and Q ≻ 0 (that is, R is positive semidefinite and Q is positive definite). This reformulation results in an equivalent optimization problem with a simple convex feasible set. We propose three strategies to solve the problem in variables ( J , R , Q ) : (i) a block coordinate descent method, (ii) a projected gradient descent method, and (iii) a fast gradient method inspired from smooth convex optimization. These methods require O ( n 3 ) operations per iteration, where n is the size of A . We show the effectiveness of the fast gradient method compared to the other approaches and to several state-of-the-art algorithms.

Authors:Shmuel Yonatan Hayoun; Tal Shima Pages: 122 - 128 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Shmuel Yonatan Hayoun, Tal Shima A linearized endgame interception scenario along a line between a single evading target and n pursuers is considered, in which the adversaries’ controls are bounded and have arbitrary-order dynamics, and the evader’s maneuvers are not known a priori to the pursuing team. To determine the merit in utilizing multiple interceptors, in terms of their capability to impose point capture, a capturability analysis is performed, presenting necessary and sufficient conditions for the feasibility of point capture for any admissible evader maneuver. It is shown that the pursuing team is capable of guaranteeing point capture if and only if it consists of at least one pursuer capable of independently imposing point capture. This requirement is independent of the number of pursuers, leading to the conclusion that it cannot be relaxed by increasing the number of interceptors or by any manner of cooperation, in terms of coordinated motion, between the pursuers.

Authors:Lantao Xing; Changyun Wen; Zhitao Liu; Hongye Su; Jianping Cai Pages: 129 - 136 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Lantao Xing, Changyun Wen, Zhitao Liu, Hongye Su, Jianping Cai In this paper, we study the problem of event-triggered control for a class of uncertain nonlinear systems subject to actuator failures. The actuator failures are allowed to be unknown and the total number of failures could be infinite. To reduce the communication burden from the controller to the actuator, a novel event-triggered control law is designed. It is proved through Lyapunov analyses that the proposed control protocol ensures that all the signals of the closed-loop system are globally bounded and the system output tracking error can exponentially converge to a residual which can be made arbitrarily small.

Authors:Jurre Hanema; Mircea Lazar; Roland Tóth Pages: 137 - 144 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Jurre Hanema, Mircea Lazar, Roland Tóth This paper presents a stabilizing tube-based MPC synthesis for LPV systems. We employ terminal constraint sets which are required to be controlled periodically contractive. Periodically (or finite-step) contractive sets are easier to compute and can be of lower complexity than “true” contractive ones, lowering the required computational effort both off-line and on-line. Under certain assumptions on the tube parameterization, recursive feasibility of the scheme is proven. Subsequently, asymptotic stability of the origin is guaranteed through the construction of a suitable terminal cost based on a novel Lyapunov-like metric for compact convex sets containing the origin. A periodic variant on the well-known homothetic tube parameterization that satisfies the necessary assumptions and yields a tractable LPV MPC algorithm is derived. The resulting MPC algorithm requires the on-line solution of a single linear program with linear complexity in the prediction horizon. The properties of the approach are demonstrated by a numerical example.

Authors:Esmaeil Naderi; K. Khorasani Pages: 165 - 178 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Esmaeil Naderi, K. Khorasani In this work, we propose and develop data-driven explicit state-space based fault detection, isolation and estimation filters that are directly identified and constructed from only the available system input–output (I/O) measurements and through only the estimated system Markov parameters. The proposed methodology does not involve a reduction step and does not require identification of the system extended observability matrix or its left null space. The performance of our proposed filters is directly related to and linearly dependent on the Markov parameters identification errors. The estimation filters operate with a subset of the system I/O data that is selected by the designer. It is shown that our proposed filters provide an asymptotically unbiased estimate by invoking a low order filter as long as the selected subsystem has a stable inverse. We have derived the estimation error dynamics in terms of the Markov parameters identification errors and have shown that they can be directly synthesized from the healthy system I/O data. Consequently, our proposed methodology ensures that the estimation errors can be effectively compensated for. Finally, we have provided several illustrative case study simulations that demonstrate and confirm the merits of our proposed schemes as compared to methodologies that are available in the literature.

Authors:Wenjun Song; Johan Markdahl; Silun Zhang; Xiaoming Hu; Yiguang Hong Pages: 193 - 201 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Wenjun Song, Johan Markdahl, Silun Zhang, Xiaoming Hu, Yiguang Hong This paper investigates the reduced attitude formation control problem for a group of rigid-body agents using feedback based on relative attitude information. Under both undirected and directed cycle graph topologies, it is shown that reversing the sign of a classic consensus protocol yields asymptotical convergence to formations whose shape depends on the parity of the group size. Specifically, in the case of even parity the reduced attitudes converge asymptotically to a pair of antipodal points and distribute equidistantly on a great circle in the case of odd parity. Moreover, when the inter-agent graph is an undirected ring, the desired formation is shown to be achieved from almost all initial states.

Authors:Anton V. Proskurnikov; Ming Cao Pages: 202 - 210 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Anton V. Proskurnikov, Ming Cao Many distributed algorithms for multi-agent coordination employ the simple averaging dynamics, referred to as the Laplacian flow. Besides the standard consensus protocols, examples include, but are not limited to, algorithms for aggregation and containment control, target surrounding, distributed optimization and models of opinion formation in social groups. In spite of their similarities, each of these algorithms has been studied using separate mathematical techniques. In this paper, we show that stability and convergence of many coordination algorithms involving the Laplacian flow dynamics follow from the general consensus dichotomy property of a special differential inequality. The consensus dichotomy implies that any solution to the differential inequality is either unbounded or converges to a consensus equilibrium. In this paper, we establish the dichotomy criteria for differential inequalities and illustrate their applications to multi-agent coordination and opinion dynamics modeling.

Authors:Gabriele Oliva; Roberto Setola; Antonio Scala Pages: 211 - 220 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Gabriele Oliva, Roberto Setola, Antonio Scala The Analytic Hierarchy Process (AHP) is a de-facto standard technique in centralized decision making. Consider a situation where there is a need to rank a set of elements or alternatives, based on their value or utility, of which we just know pairwise relative information, i.e., the ratio of their values. AHP proved an effective tool to retrieve the value of each element, being able to handle also relative information affected by distortions, subjective biases and intransitivity. A downside of AHP, however, is that it requires complete information, i.e., knowledge on all pairs. In this paper, we extend the applicability of the AHP technique to the case of sparse information, i.e., when only a limited amount of information is available, and such an information corresponds to an undirected connected graph. We complement our sparse framework by developing novel criteria and metrics to evaluate the degree of consistency of the data at hand. Moreover, exploiting the proposed framework, we also provide a distributed formulation of AHP in which a set of agents, interacting through an undirected graph, are able to compute their own values (e.g., for ranking or leader election purposes), by only knowing the ratio of their values with respect to their neighbors. To this end, we develop a novel algorithm to let each agent i compute, the dominant eigenvalue and the i th component of the corresponding eigenvector of the sparse AHP matrix. We conclude the paper with a simulation campaign that numerically demonstrates the effectiveness of the proposed approach.

Authors:Riccardo Sven Risuleo; Giulio Bottegal; Håkan Hjalmarsson Pages: 234 - 247 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Riccardo Sven Risuleo, Giulio Bottegal, Håkan Hjalmarsson Hammerstein systems are the series composition of a static nonlinear function and a linear dynamic system. In this work, we propose a nonparametric method for the identification of Hammerstein systems. We adopt a kernel-based approach to model the two components of the system. In particular, we model the nonlinear function and the impulse response of the linear block as Gaussian processes with suitable kernels. The kernels can be chosen to encode prior information about the nonlinear function and the system. Following the empirical Bayes approach, we estimate the posterior mean of the impulse response using estimates of the nonlinear function, of the hyperparameters, and of the noise variance. These estimates are found by maximizing the marginal likelihood of the data. This maximization problem is solved using an iterative scheme based on the expectation-conditional maximization, which is a variation of the standard expectation–maximization method for solving maximum-likelihood problems. We show the effectiveness of the proposed identification scheme in some simulation experiments.

Authors:Maarten Schoukens; Koen Tiels Pages: 272 - 292 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Maarten Schoukens, Koen Tiels Block-oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use. Many different identification approaches were developed over the years to estimate the parameters of a wide range of block-oriented nonlinear models. One class of these approaches uses linear approximations to initialize the identification algorithm. The best linear approximation framework and the ϵ -approximation framework, or equivalent frameworks, allow the user to extract important information about the system, guide the user in selecting good candidate model structures and orders, and prove to be a good starting point for nonlinear system identification algorithms. This paper gives an overview of the different block-oriented nonlinear models that can be identified using linear approximations, and of the identification algorithms that have been developed in the past. A non-exhaustive overview of the most important other block-oriented nonlinear system identification approaches is also provided throughout this paper.

Authors:Arash Kh. Sichani; Igor G. Vladimirov; Ian R. Petersen Pages: 314 - 326 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Arash Kh. Sichani, Igor G. Vladimirov, Ian R. Petersen This paper is concerned with coherent quantum linear quadratic Gaussian (CQLQG) control. The problem is to find a stabilizing measurement-free quantum controller for a quantum plant so as to minimize a mean square cost for the fully quantum closed-loop system. The plant and controller are open quantum systems interconnected through bosonic quantum fields. In comparison with the observation–actuation structure of classical controllers, coherent quantum feedback is less invasive to the quantum dynamics. The plant and controller variables satisfy the canonical commutation relations (CCRs) of a quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to such oscillators, these QSDEs must satisfy physical realizability (PR) conditions in the form of quadratic constraints on the state-space matrices, reflecting the CCR preservation in time. The symmetry of the problem is taken into account by introducing equivalence classes of coherent quantum controllers generated by symplectic similarity transformations. We discuss a modified gradient flow, which is concerned with norm-balanced realizations of controllers. A line-search gradient descent algorithm with adaptive stepsize selection is proposed for the numerical solution of the CQLQG control problem. The algorithm finds a local minimum of the LQG cost over the parameters of the Hamiltonian and coupling operators of a stabilizing coherent quantum controller, thus taking the PR constraints into account. A convergence analysis of the algorithm is presented. Numerical examples of designing locally optimal CQLQG controllers are provided in order to demonstrate the algorithm performance.

Authors:T.W.U. Madhushani; D.H.S. Maithripala; J.V. Wijayakulasooriya; J.M. Berg Pages: 327 - 338 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): T.W.U. Madhushani, D.H.S. Maithripala, J.V. Wijayakulasooriya, J.M. Berg A spherical robot consists of an externally spherical rigid body rolling on a two-dimensional surface, actuated by an auxiliary mechanism. For a class of actuation mechanisms, we derive a controller for the geometric center of the sphere to asymptotically track any sufficiently smooth reference trajectory, with robustness to bounded, constant uncertainties in the inertial properties of the sphere and actuation mechanism, and to constant disturbance forces including, for example, from constant inclination of the rolling surface. The sphere and actuator are modeled as distinct systems, coupled by reaction forces. It is assumed that the actuator can provide three independent control torques, and that the actuator center of mass remains at a constant distance from the geometric center of the sphere. We show that a necessary and sufficient condition for such a controller to exist is that for any constant disturbance torque acting on the sphere there is a constant input such that the sphere and the actuator mechanism has a stable relative equilibrium. A geometric PID controller guarantees robust, semi-global, locally exponential stability for the position tracking error of the geometric center of the sphere, while ensuring that actuator velocities are bounded.

Authors:Mamadou Diagne; Nikolaos Bekiaris-Liberis; Miroslav Krstic Pages: 362 - 373 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Mamadou Diagne, Nikolaos Bekiaris-Liberis, Miroslav Krstic For nonlinear systems, we develop a PDE-based predictor-feedback control design, which compensates actuator dynamics, governed by a transport PDE with outlet boundary-value-dependent propagation velocity. Global asymptotic stability under the predictor-feedback control law is established assuming spatially uniform strictly positive transport velocity. The stability proof is based on a Lyapunov-like argument and employs an infinite-dimensional backstepping transformation that is introduced. An equivalent representation of the transport PDE/nonlinear ODE cascade via a nonlinear system with an input delay that is defined implicitly through an integral of the past input is also provided and the equivalent predictor-feedback control design for the delay system is presented. The validity of the proposed controller is illustrated applying a predictor-feedback “bang–bang” boundary control law to a PDE model of a production system with a queue. Consistent simulation results are provided that support the theoretical developments.

Authors:Giorgio Battistelli; Luigi Chisci; Stefano Gherardini Pages: 374 - 385 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Giorgio Battistelli, Luigi Chisci, Stefano Gherardini The paper addresses state estimation for linear discrete-time systems with binary (threshold) measurements. A Moving Horizon Estimation (MHE) approach is followed and different estimators, characterized by two different choices of the cost function to be minimized and/or by the possible inclusion of constraints, are proposed. Specifically, the cost function is either quadratic, when only the information pertaining to the threshold-crossing instants is exploited, or piece-wise quadratic, when all the available binary measurements are taken into account. Stability results are provided for the proposed MHE algorithms in the presence of unknown but bounded disturbances and measurement noise. Performance of the proposed techniques is also assessed by means of simulation examples.

Authors:Ying Tang; Guilherme Mazanti Pages: 386 - 396 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Ying Tang, Guilherme Mazanti This paper is concerned with a class of coupled ODE/PDE systems with two time scales. The fast constant time scale is modeled by a small positive perturbation parameter. First, we state a general sufficient stability condition for such systems. This condition is also sufficient for the stability of the reduced and boundary-layer subsystems. However, counterexamples illustrate that the converse is not true. Next, we study the stability of such systems by taking into account the fact that the perturbation parameter is sufficiently small. For linear ODE coupled with fast hyperbolic PDE systems the stability of both subsystems implies the stability of the full system. On the other hand, a counterexample shows that the full system can be unstable even though the two subsystems are stable for a PDE coupled with fast ODE system. Numerical simulations on academic examples are proposed. Moreover, an application to boundary control of a gas flow transport system is used to illustrate the theoretical result.

Authors:Zhiyong Sun; Shaoshuai Mou Brian D.O. Anderson Changbin Abstract: Publication date: January 2018 Source:Automatica, Volume 87 Author(s): Zhiyong Sun, Shaoshuai Mou, Brian D.O. Anderson, Changbin Yu In this paper we discuss and discover several conservation and associated decay laws in distributed coordination control systems, in particular in formation shape control systems. Specifically, we reveal conservations of linear momentum and angular momentum for gradient-based multi-agent formation systems modelled by single integrators, and show several corresponding conservation/decay laws for double-integrator formation stabilization systems and double-integrator flocking systems, respectively. By exploiting translation and rotation symmetry properties and insights from Noether’s theorem, we further establish a multi-agent version of the relation between symmetry and conservation laws for gradient-based coordination systems derived from general potential functions, from which we generalize the conservation/decay laws to more general networked coordination control systems. The results hold in ambient spaces of any dimensions, and we focus on the 2-D and 3-D cases due to their natural interpretation as positions of agents.