Dynamic Event-Triggered State Estimation for Discrete-Time Singularly Perturbed Systems With Distributed Time-Delays
TL;DR: This paper addresses the state estimation problem for a class of discrete-time singularly perturbed systems with distributed time-delays with dynamic event-triggered scheme and proposes a design algorithm for the desired state estimator ensuring that the error dynamics is exponentially mean-square ultimately bounded.
Abstract: This paper is concerned with the state estimation problem for a class of discrete-time singularly perturbed systems with distributed time-delays. During the data transmission through a network channel of limited bandwidth, for the sake of collision avoidance and energy saving, a dynamic event-triggered scheme is employed to schedule the data communication from the sensors to the designed estimator. First, for a given singular perturbation parameter (SPP), by constructing a novel Lyapunov–Krasovskii SPP-dependent functional, sufficient conditions are obtained to guarantee the exponentially mean-square ultimate boundedness of the error dynamics of the state estimation. Furthermore, in the case that the SPP does not exceed a predefined upper bound, a design algorithm is developed for the desired state estimator ensuring that the error dynamics is exponentially mean-square ultimately bounded. In this case, by solving certain matrix inequalities, the estimator gain is characterized without needing to know the exact SPP (as long as it stays below the given upper bound). Moreover, the ultimate bound of the error dynamics is estimated. Finally, simulation results are given to confirm the validity and advantages of the proposed design scheme of the state estimator.
Citations
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TL;DR: The aim is to design a distributed filter for each sensor node such that an upper bound on the filtering error variance is guaranteed and subsequently minimized at each iteration under the dynamic event-triggered transmission protocol.
136 citations
TL;DR: In this paper , a novel double-layer switching regulation containing Markov chain and persistent dwell-time switching regulation (PDTSR) is used to solve the H∞ synchronization issue for singularly perturbed coupled neural networks (SPCNNs).
Abstract: This work explores the H∞ synchronization issue for singularly perturbed coupled neural networks (SPCNNs) affected by both nonlinear constraints and gain uncertainties, in which a novel double-layer switching regulation containing Markov chain and persistent dwell-time switching regulation (PDTSR) is used. The first layer of switching regulation is the Markov chain to characterize the switching stochastic properties of the systems suffering from random component failures and sudden environmental disturbances. Meanwhile, PDTSR, as the second-layer switching regulation, is used to depict the variations in the transition probability of the aforementioned Markov chain. For systems under double-layer switching regulation, the purpose of the addressed issue is to design a mode-dependent synchronization controller for the network with the desired controller gains calculated by solving convex optimization problems. As such, new sufficient conditions are established to ensure that the synchronization error systems are mean-square exponentially stable with a specified level of the H∞ performance. Eventually, the solvability and validity of the proposed control scheme are illustrated through a numerical simulation.
128 citations
TL;DR: In this paper, the analysis and synthesis issues have gained widespread attention for complex dynamical networks (CDNs) over the past few years, and some challenges including protocol-based scheduling, s...
Abstract: The analysis and synthesis issues have gained widespread attention for complex dynamical networks (CDNs) over the past few years. Accordingly, some challenges including protocol-based scheduling, s...
125 citations
TL;DR: This article addresses the investigation of sliding-mode control (SMC) for slow-sampling singularly perturbed systems (SPSs) with Markov jump parameters and the applicability of the SMC strategy is verified by a numerical example and a practical electric circuit model.
Abstract: This article addresses the investigation of sliding-mode control (SMC) for slow-sampling singularly perturbed systems (SPSs) with Markov jump parameters. As a new attempt, the SMC strategy is considered in the study of discrete-time Markov jump SPSs. Subsequently, in order to design a sliding-mode controller to ensure the stability of the proposed system, a novel integral sliding surface is constructed, and an SMC law is synthesized to ensure the reachability of the sliding surface. Through the utilization of Lyapunov stability and SMC theory, sufficient conditions are derived to ensure the state trajectories of the system are driven to a predefined sliding surface and the closed-loop sliding mode dynamics are stochastically stable. Finally, the applicability of the proposed SMC strategy is verified by a numerical example and a practical electric circuit model.
97 citations
TL;DR: The proposed ET condition together with an adaptive ET threshold coefficient is constructed to guarantee the UUB of the closed-loop networked control system through the Lyapunov stability theory, thereby largely easing the network communication load.
Abstract: This paper proposes a novel event-triggered (ET) adaptive neural control scheme for a class of discrete-time nonlinear systems in a strict-feedback form. In the proposed scheme, the ideal control input is derived in a recursive design process, which relies on system states only and is unrelated to virtual control laws. In this case, the high-order neural networks (NNs) are used to approximate the ideal control input (but not the virtual control laws), and then the corresponding adaptive neural controller is developed under the ET mechanism. A modified NN weight updating law, nonperiodically tuned at triggering instants, is designed to guarantee the uniformly ultimate boundedness (UUB) of NN weight estimates for all sampling times. In virtue of the bounded NN weight estimates and a dead-zone operator, the ET condition together with an adaptive ET threshold coefficient is constructed to guarantee the UUB of the closed-loop networked control system through the Lyapunov stability theory, thereby largely easing the network communication load. The proposed ET condition is easy to implement because of the avoidance of: 1) the use of the intermediate ET conditions in the backstepping procedure; 2) the computation of virtual control laws; and 3) the redundant triggering of events when the system states converge to a desired region. The validity of the presented scheme is demonstrated by simulation results.
89 citations
Additional excerpts
...the existing control methods [27], [29], [49]....
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References
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Book•
01 Jan 1986TL;DR: This SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications.
Abstract: From the Publisher:
Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications.
This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point.
Audience
Control engineers and graduate students who seek an introduction to singular perturbation methods in control will find this text useful. The book also provides research workers with sketches of problems in the areas of robust, adaptive, stochastic, and nonlinear control. No previous knowledge of singular perturbation techniques is assumed.
About the Authors
Petar Kokotovic is Director of the Center for Control Engineering and Computation at the University of California, Santa Barbara. Hassan K. Khalil is Professor of Electrical and Computer Engineering at Michigan State University. John O'Reilly is Professor of Electronics and Electrical Engineering at the University of Glasgow, Scotland.
2,446 citations
TL;DR: Simulation results have shown that the proposed event-triggering scheme is superior to some existing event- triggering schemes in the literature.
Abstract: This note is concerned with event-triggered H∞ controller design for networked control systems. A novel event-triggering scheme is proposed, which has some advantages over some existing schemes. A delay system model for the analysis is firstly constructed by investigating the effect of the network transmission delay. Then, based on this model, criteria for stability with an H∞ norm bound and criteria for co-designing both the feedback gain and the trigger parameters are derived. These criteria are formulated in terms of linear matrix inequalities. Simulation results have shown that the proposed event-triggering scheme is superior to some existing event-triggering schemes in the literature.
1,326 citations
"Dynamic Event-Triggered State Estim..." refers background in this paper
...Another class of protocols, whose aim is to lower the signal transmission frequency according to certain event-triggering mechanism, is the so-called event-triggered scheme (ETS) that has recently gained considerable research interest: see [22], [38], and [42] for some representative results....
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TL;DR: In this paper, the authors present a new class of event triggering mechanisms for event-triggered control systems characterized by the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event triggering mechanism.
Abstract: In this technical note, we present a new class of event triggering mechanisms for event-triggered control systems. This class is characterized by the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event triggering mechanism. The stability of the resulting closed-loop system is proved and the influence of design parameters on the decay rate of the Lyapunov function is discussed. For linear systems, we establish a lower bound on the inter-execution time as a function of the parameters. The influence of these parameters on a quadratic integral performance index is also studied. Some simulation results are provided for illustration of the theoretical claims.
965 citations
Posted Content•
TL;DR: This class is characterized by the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event triggering mechanism, and a lower bound on the inter-execution time as a function of the parameters is established.
Abstract: In this paper, we present a new class of event triggering mechanisms for event-triggered control systems. This class is characterized by the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event triggering mechanism. The stability of the resulting closed loop system is proved and the influence of design parameters on the decay rate of the Lyapunov function is discussed. For linear systems, we establish a lower bound on the inter-execution time as a function of the parameters. The influence of these parameters on a quadratic integral performance index is also studied. Some simulation results are provided for illustration of the theoretical claims.
744 citations
"Dynamic Event-Triggered State Estim..." refers background in this paper
...Recently, with hope to further save communication resource, the so-called dynamic ETS (DETS) has been designed in [9] for a continuous-time networked system by adjusting the threshold parameter dynamically at each checking instant....
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01 Oct 2008
TL;DR: A synchronization problem is investigated for an array of coupled complex discrete-time networks with the simultaneous presence of both the discrete and distributed time delays and an LMI approach is developed for the state estimation problem.
Abstract: In this paper, a synchronization problem is investigated for an array of coupled complex discrete-time networks with the simultaneous presence of both the discrete and distributed time delays. The complex networks addressed which include neural and social networks as special cases are quite general. Rather than the commonly used Lipschitz-type function, a more general sector-like nonlinear function is employed to describe the nonlinearities existing in the network. The distributed infinite time delays in the discrete-time domain are first defined. By utilizing a novel Lyapunov-Krasovskii functional and the Kronecker product, it is shown that the addressed discrete-time complex network with distributed delays is synchronized if certain linear matrix inequalities (LMIs) are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that, for all admissible discrete and distributed delays, the dynamics of the estimation error is guaranteed to be globally asymptotically stable. Again, an LMI approach is developed for the state estimation problem. Two simulation examples are provided to show the usefulness of the proposed global synchronization and state estimation conditions. It is worth pointing out that our main results are valid even if the nominal subsystems within the network are unstable.
486 citations
"Dynamic Event-Triggered State Estim..." refers background in this paper
...Lemma 3 [18]: Let a matrix Q ≥ 0, scalar constants ai, i ∈ Z, and positive integer τ be given....
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