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: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:Giulio Bottegal; Håkan Hjalmarsson; Gianluigi Pillonetto Pages: 145 - 152 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Giulio Bottegal, Håkan Hjalmarsson, Gianluigi Pillonetto In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation–maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data.

Authors:Hasan A. Poonawala; Mark W. Spong Pages: 153 - 157 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Hasan A. Poonawala, Mark W. Spong Nonholonomic wheeled mobile robots are often required to implement control algorithms designed for holonomic kinematic systems. This creates a velocity tracking problem for an actual wheeled mobile robot. In this paper, we investigate the issue of tracking a desired velocity in the least amount of time, for a differential drive nonholonomic wheeled mobile robot with torque inputs. The Pontryagin Maximum Principle provides time-optimal controls that must be implemented as open-loop commands to the motors. We propose two discontinuous state-based feedback control laws, such that the associated closed-loop systems track a desired velocity in minimum time. The feedback control laws are rigorously shown to produce only time-optimal trajectories, by constructing a regular synthesis for each control law. The availability of these time-optimal feedback control laws makes re-computation of open-loop time-optimal controls (due to changes in the desired velocity or input disturbances) unnecessary.

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:Shu Liang; Peng Yi; Yiguang Hong Pages: 179 - 185 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Shu Liang, Peng Yi, Yiguang Hong In this paper, we study a distributed continuous-time design for aggregative games with coupled constraints in order to seek the generalized Nash equilibrium by a group of agents via simple local information exchange. To solve the problem, we propose a distributed algorithm based on projected dynamics and non-smooth tracking dynamics, even for the case when the interaction topology of the multi-agent network is time-varying. Moreover, we prove the convergence of the non-smooth algorithm for the distributed game by taking advantage of its special structure and also combining the techniques of the variational inequality and Lyapunov function.

Authors:Francisco Javier Bejarano; Gang Zheng Pages: 186 - 192 Abstract: Publication date: November 2017 Source:Automatica, Volume 85 Author(s): Francisco Javier Bejarano, Gang Zheng In this paper a general class of linear systems with time-delays is considered, which includes linear classical systems, linear systems with commensurate delays, neutral systems and singular systems with delays. After given a formal definition of functional backward observability (BO), an easily testable condition is found. The fulfillment of the obtained condition allows for the reconstruction of the trajectories of the system under consideration using the actual and past values of the system output and some of its derivatives. The methodology we follow consists in an iterative algorithm based upon the classical Silverman algorithm used for inversion of linear systems. By using basic module theory we manage to prove that the proposed algorithm is convergent. A direct application of studying functional observability is that a condition can be derived for systems with distributed delays also, we do this as a case of study. The obtained results are illustrated by two examples, one is merely academic but illustrates clearly the kind of systems which the proposed methodology works for and the other is a practical system with distributed delays.

Authors:S. Sepehr Tabatabaei; Heidar Ali Talebi; Mahdi Tavakoli Pages: 1 - 9 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): S. Sepehr Tabatabaei, Heidar Ali Talebi, Mahdi Tavakoli This paper proposes the design of a simultaneous order estimator and state observer for non-integer time-varying order linear systems. Several lemmas and theorems pertaining to the stability of variable order systems are provided first. Next, a theorem proposes an order/state estimator for linear variable order systems. Then, a simulation study is presented to verify the theoretical results.

Authors:Jinling Liang; Hongwei Chen; Yang Liu Pages: 10 - 16 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Jinling Liang, Hongwei Chen, Yang Liu This paper deals with the algorithms for state feedback stabilization of Boolean control networks (BCNs). By resorting to the semi-tensor product (STP) technique, the labelled digraph that can be used to completely characterize the dynamics of BCNs is derived, which leads to an equivalent graphical description for the stabilization of BCNs. What is more interesting is the fact that the existence of a state feedback control law stabilizing the BCN to some given equilibrium point can be characterized in terms of its spanning in-tree. Consequently, two in-tree search algorithms, namely, the breadth-first search and the depth-first search, are proposed to design the state feedback stabilizing law when global stabilization is feasible. Besides, some basic properties about the tree-search algorithms are addressed. A biological example is employed to illustrate the applicability and usefulness of the developed algorithms.

Authors:Kim Batselier; Zhongming Chen; Ngai Wong Pages: 17 - 25 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Kim Batselier, Zhongming Chen, Ngai Wong This article introduces a Tensor Network Kalman filter, which can estimate state vectors that are exponentially large without ever having to explicitly construct them. The Tensor Network Kalman filter also easily accommodates the case where several different state vectors need to be estimated simultaneously. The key lies in rewriting the standard Kalman equations as tensor equations and then implementing them using Tensor Networks, which effectively transforms the exponential storage cost and computational complexity into a linear one. We showcase the power of the proposed framework through an application in recursive nonlinear system identification of high-order discrete-time multiple-input multiple-output (MIMO) Volterra systems. The identification problem is transformed into a linear state estimation problem wherein the state vector contains all Volterra kernel coefficients and is estimated using the Tensor Network Kalman filter. The accuracy and robustness of the scheme are demonstrated via numerical experiments, which show that updating the Kalman filter estimate of a state vector of length 109 and its covariance matrix takes about 0.007 s on a standard desktop computer in Matlab.

Authors:Kim Batselier; Zhongming Chen; Ngai Wong Pages: 26 - 35 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Kim Batselier, Zhongming Chen, Ngai Wong This article introduces two Tensor Network-based iterative algorithms for the identification of high-order discrete-time nonlinear multiple-input multiple-output (MIMO) Volterra systems. The system identification problem is rewritten in terms of a Volterra tensor, which is never explicitly constructed, thus avoiding the curse of dimensionality. It is shown how each iteration of the two identification algorithms involves solving a linear system of low computational complexity. The proposed algorithms are guaranteed to monotonically converge and numerical stability is ensured through the use of orthogonal matrix factorizations. The performance and accuracy of the two identification algorithms are illustrated by numerical experiments, where accurate degree-10 MIMO Volterra models are identified in about 1 s using Matlab on a 3.3 GHz quad-core desktop computer with 16 GB RAM.

Authors:Yang Liu; Bowen Li; Hongwei Chen; Jinde Cao Pages: 36 - 42 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Yang Liu, Bowen Li, Hongwei Chen, Jinde Cao This paper is devoted to studying function perturbations on the transition matrix and topological structure of a singular Boolean network (SBN) via the semi-tensor product of matrices. First, the algebraic form of an SBN is given, and we discuss how the transition matrix of the SBN changes under function perturbations. Then the local uniqueness of solutions to the SBN is studied, under which the impacts of function perturbations on the topological structure are investigated. Finally, examples are given to show the effectiveness of the obtained results.

Authors:Anton A. Stoorvogel; Ali Saberi; Meirong Zhang Pages: 43 - 47 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Anton A. Stoorvogel, Ali Saberi, Meirong Zhang This paper derives conditions on the agents for the existence of a protocol which achieves synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling, where the communication network is directed and weighted. These solvability conditions are necessary and sufficient for single-input agents and sufficient for multi-input agents. The solvability conditions reveal that the synchronization problem is primarily solvable for two classes of agents. This first class consists of at most weakly unstable agents (i.e. agents have all eigenvalues in the closed left half plane) and the second class consists of at most weakly non-minimum-phase agents (i.e. agents have all zeros in the closed left half plane). Under our solvability condition, we provide in this paper a design, utilizing H ∞ optimal control.

Authors:Dario Bauso Pages: 48 - 55 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Dario Bauso This paper investigates the relation between cooperation, competition, and local interactions in large distributed multi-agent systems. The main contribution is the game-theoretic problem formulation and solution approach based on the new framework of distributed approachability, and the study of the convergence properties of the resulting game model. Approachability theory is the theory of two-player repeated games with vector payoffs, and distributed approachability is here presented for the first time as an extension to the case where we have a team of agents cooperating against a team of adversaries under local information and interaction structure. The game model turns into a nonlinear differential inclusion, which after a proper design of the control and disturbance policies, presents a consensus term and an exogenous adversarial input. Local interactions enter into the model through a graph topology and the corresponding graph-Laplacian matrix. Given the above model, we turn the original questions on cooperation, competition, and local interactions, into convergence properties of the differential inclusion. In particular, we prove convergence and exponential convergence conditions around zero under general Markovian strategies. We illustrate our results in the case of decentralized organizations with multiple decision-makers.

Authors:Dmitry V. Balandin; Mark M. Kogan Pages: 56 - 61 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Dmitry V. Balandin, Mark M. Kogan A multi-objective disturbance attenuation problem is considered as a novel framework for control and filtering problems under multiple exogenous disturbances. There are N potentially possible disturbance inputs of a system on each of which may act a disturbance from a certain class. A disturbance attenuation level is defined for each channel as an induced norm of the operator mapping signals of the corresponding class to the objective output of the system. Necessary conditions of the Pareto optimality are derived. It is established that the optimal solutions with respect to a multi-objective cost parameterized by weights from an N -dimensional simplex are Pareto suboptimal solutions and their relative losses compared to the Pareto optimal ones do not exceed 1 − N ∕ N . These results are extended to the case when the disturbances acting on different inputs are combined into coalitions. The approach is applied to multiple classes of L 2 -bounded and impulsive disturbances for which the H ∞ ∕ γ 0 optimal controllers as the Pareto suboptimal solutions are synthesized in terms of linear matrix inequalities (LMIs). Illustrative examples demonstrate the effectiveness of the approach proposed.

Authors:Mohammad Soltani; Abhyudai Singh Pages: 62 - 69 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Mohammad Soltani, Abhyudai Singh Stochastic Hybrid Systems (SHS) constitute an important class of mathematical models that integrate discrete stochastic events with continuous dynamics. The time evolution of statistical moments is generally not closed for SHS, in the sense that the time derivative of the lower-order moments depends on higher-order moments. Here, we identify an important class of SHS where moment dynamics is automatically closed, and hence moments can be computed exactly by solving a system of coupled differential equations. This class is referred to as linear time-triggered SHS (TTSHS), where the state evolves according to a linear dynamical system. Stochastic events occur at discrete times and the intervals between them are independent random variables that follow a general class of probability distributions. Moreover, whenever the event occurs, the state of the SHS changes randomly based on a probability distribution. Our approach relies on embedding a Markov chain based on phase-type processes to model timing of events, and showing that the resulting system has closed moment dynamics. Interestingly, we identify a subclass of linear TTSHS, where the first and second-order moments depend only on the mean time interval between events, and invariant of higher-order statistics of event timing. TTSHS are used to model examples drawn from cell biology and nanosensors, providing novel insights into how noise is regulated in these systems.

Authors:Chirayu D. Athalye; Debasattam Pal; Harish K. Pillai Pages: 70 - 78 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Chirayu D. Athalye, Debasattam Pal, Harish K. Pillai In this paper, we analyze ℓ 2 -stability of infinite dimensional discrete autonomous systems given in a state space form with state transition matrix being a Laurent polynomial matrix A ( σ , σ − 1 ) in the shift operator σ . We give sufficient conditions and necessary conditions for ℓ 2 -stability of such systems. We then use the theory of ℓ 2 -stability, thus developed, to analyze ℓ 2 -stability of discrete 2-D autonomous systems. We achieve this by showing how a discrete 2-D autonomous system can be converted to an equivalent infinite dimensional state space discrete autonomous system, where the state transition matrix turns out to be a Laurent polynomial matrix in the shift operator. Finally, we provide some easy-to-check numerical tests for ℓ 2 -stability of the above-mentioned type of systems.

Authors:Maria Elena Valcher; Irene Zorzan Pages: 79 - 85 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Maria Elena Valcher, Irene Zorzan In this paper we investigate the consensus problem under arbitrary switching for homogeneous multi-agent systems with switching communication topology, by assuming that each agent is described by a single-input stabilizable state–space model and that the communication graph is connected at every time instant. Under these assumptions, we construct a common quadratic positive definite Lyapunov function for the switched system describing the evolution of the disagreement vector, thus showing that the agents always reach consensus. In addition, the proof leads to the explicit construction of a constant state-feedback matrix that allows the multi-agent system to achieve consensus.

Authors:Bahare Kiumarsi; Frank L. Lewis Pages: 86 - 94 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Bahare Kiumarsi, Frank L. Lewis This paper presents an optimal model-free solution to the output synchronization of heterogeneous multi-agent discrete-time systems. First, local discounted performance functions are defined for all agents and the optimal synchronization control protocols are found by solving a set of algebraic Riccati equations (AREs) and without requiring the explicit solution to the output regulator equations. It is shown that the proposed method implicitly solves the output regulator equations and therefore solves the output synchronization problem, provided that the discount factor is bigger than a lower bound. This formulation enables us to develop a Q -learning algorithm to solve the AREs using only measured data and so find the optimal distributed control protocols for each agent without requiring complete knowledge of the agents’ or leader’s dynamics. It is shown that the combination of a distributed adaptive observer and the controller guarantees synchronization. The relationship between the standard solution and the proposed solution is also shown. A simulation example is given to show the effectiveness of the proposed method.

Authors:Jean-Michel Coron; Long Hu; Guillaume Olive Pages: 95 - 100 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Jean-Michel Coron, Long Hu, Guillaume Olive This paper is devoted to a simple and new proof on the optimal finite control time for general linear coupled hyperbolic system by using boundary feedback on one side. The feedback control law is designed by first using a Volterra transformation of the second kind and then using an invertible Fredholm transformation. Both existence and invertibility of the transformations are easily obtained.

Authors:Hui Xiao; Siyang Gao; Loo Hay Lee Pages: 117 - 127 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Hui Xiao, Siyang Gao, Loo Hay Lee Motivated by the practical needs in simulation optimization, this paper considers the problem of selecting the best m and worst n designs from a total of k alternatives based on their mean performance values, which are unknown and can only be estimated via simulation. In order to improve the efficiency of simulation, this research characterizes an asymptotically optimal allocation of simulation replications among the k designs such that the probability of correctly selecting the best m and worst n designs can be maximized, and develops a corresponding selection procedure for implementation purpose. The efficiency of the proposed procedure is demonstrated via numerical experiments.

Authors:Valery Ugrinovskii; Cedric Langbort Pages: 128 - 141 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Valery Ugrinovskii, Cedric Langbort The paper introduces a class of zero-sum games between the adversary and controller as a scenario for a ‘denial of service’ in a networked control system. The communication link is modelled as a set of transmission regimes controlled by a strategic jammer whose intention is to wage an attack on the plant by choosing a most damaging regime-switching strategy. We demonstrate that even in the one-step case, the introduced games admit a saddle-point equilibrium, at which the jammer’s optimal policy is to randomize in a region of the plant’s state space, thus requiring the controller to undertake a nontrivial response which is different from what one would expect in a standard stochastic control problem over a packet dropping link. The paper derives conditions for the introduced games to have such a saddle-point equilibrium. Furthermore, we show that in more general multi-stage games, these conditions provide ‘greedy’ jamming strategies for the adversary.

Authors:Alessandro Falsone; Kostas Margellos; Simone Garatti; Maria Prandini Pages: 149 - 158 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Alessandro Falsone, Kostas Margellos, Simone Garatti, Maria Prandini We study distributed optimization in a cooperative multi-agent setting, where agents have to agree on the usage of shared resources and can communicate via a time-varying network to this purpose. Each agent has its own decision variables that should be set so as to minimize its individual objective function subject to local constraints. Resource sharing is modeled via coupling constraints that involve the non-positivity of the sum of agents’ individual functions, each one depending on the decision variables of one single agent. We propose a novel distributed algorithm to minimize the sum of the agents’ objective functions subject to both local and coupling constraints, where dual decomposition and proximal minimization are combined in an iterative scheme. Notably, privacy of information is guaranteed since only the dual optimization variables associated with the coupling constraints are exchanged by the agents. Under convexity assumptions, jointly with suitable connectivity properties of the communication network, we are able to prove that agents reach consensus to some optimal solution of the centralized dual problem counterpart, while primal variables converge to the set of optimizers of the centralized primal problem. The efficacy of the proposed approach is demonstrated on a plug-in electric vehicles charging problem.

Authors:Mahyar Fazlyab; Florian Dörfler; Victor M. Preciado Pages: 181 - 189 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Mahyar Fazlyab, Florian Dörfler, Victor M. Preciado This paper studies the problem of designing networks of nonidentical coupled oscillators in order to achieve a desired level of phase cohesiveness, defined as the maximum asymptotic phase difference across the edges of the network. In particular, we consider the following two design problems: (i) the nodal-frequency design problem, in which we tune the natural frequencies of the oscillators given the topology of the network, and (ii) the (robust) edge-weight design problem, in which we design the edge weights assuming that the natural frequencies are given (or belong to a given convex uncertainty set). For both problems, we optimize an objective function of the design variables while considering a desired level of phase cohesiveness as our design constraint. This constraint defines a convex set in the nodal-frequency design problem. In contrast, in the edge-weight design problem, the phase cohesiveness constraint yields a non-convex set, unless the underlying network is either a tree or an arbitrary graph with identical edge weights. We then propose a convex semidefinite relaxation to approximately solve the (non-convex) edge-weight design problem for general (possibly cyclic) networks with nonidentical edge weights. We illustrate the applicability of our results by analyzing several network design problems of practical interest, such as power redispatch in power grids, sparse network design, (robust) network design for distributed wireless analog clocks, and the detection of edges leading to the Braess’ paradox in power grids.

Authors:Xiaoqing Cheng; Takeyuki Tamura; Wai-Ki Ching; Tatsuya Akutsu Pages: 205 - 213 Abstract: Publication date: October 2017 Source:Automatica, Volume 84 Author(s): Xiaoqing Cheng, Takeyuki Tamura, Wai-Ki Ching, Tatsuya Akutsu Determining the minimum number of sensor nodes to observe the internal state of the whole system is important in analysis of complex networks. However, existing studies suggest that a large number of sensor nodes are needed to know the whole internal state. In this paper, we focus on identification of a small set of sensor nodes to discriminate statically and periodically steady states using the Boolean network model where steady states are often considered to correspond to cell types. In other words, we seek a minimum set of nodes to discriminate singleton and periodic attractors. We prove that one node is not necessarily enough but two nodes are always enough to discriminate two periodic attractors by using the Chinese remainder theorem. Based on this, we present an algorithm to determine the minimum number of nodes to discriminate all given attractors. We also present a much more efficient algorithm to discriminate singleton attractors. The results of computational experiments suggest that attractors in realistic Boolean networks can be discriminated by observing the states of only a small number of nodes.