Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems
TL;DR: A continuous feedback controller is designed for the switched system, which guarantees that asymptotic output tracking is achieved without transgression of the constraints and all closed-loop signals remain bounded, provided that the initial states are feasible.
About: This article is published in Systems & Control Letters.The article was published on 2013-10-01. It has received 291 citations till now. The article focuses on the topics: Lyapunov function & Backstepping.
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TL;DR: This paper investigates an adaptive fuzzy tracking control design problem for single-input and single-output uncertain nonstrict feedback nonlinear systems and proposes both adaptive fuzzy state feedback and observer-based output feedback control designs.
Abstract: This paper investigates an adaptive fuzzy tracking control design problem for single-input and single-output uncertain nonstrict feedback nonlinear systems. For the cases of the states measurable and the states immeasurable, fuzzy logic systems are separately adopted to approximate the unknown nonlinear functions or model the uncertain nonlinear systems. In the unified framework of adaptive backstepping control design, both adaptive fuzzy state feedback and observer-based output feedback control design schemes are proposed. The stability of the closed-loop systems is proved by using Lyapunov function theory. The simulation examples are provided to confirm the effectiveness of the proposed control methods.
382 citations
TL;DR: In this technical note, the problem of switching stabilization for slowly switched linear systems is investigated and sufficient condition of stabilization for switched systems with all stable subsystems under MDADT switching is given.
Abstract: In this technical note, the problem of switching stabilization for slowly switched linear systems is investigated. In particular, the considered systems can be composed of all unstable subsystems. Based on the invariant subspace theory, the switching signal with mode-dependent average dwell time (MDADT) property is designed to exponentially stabilize the underlying system. Furthermore, sufficient condition of stabilization for switched systems with all stable subsystems under MDADT switching is also given. The correctness and effectiveness of the proposed approaches are illustrated by a numerical example.
300 citations
Cites background from "Barrier Lyapunov functions for the ..."
...So far, many results on behavior analysis, property characterization [28] and control synthesis [11], [21], [24], [29] for various types of switched systems have been studied due to their numerous applications....
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TL;DR: The problem of asymptotic tracking control for a class of uncertain switched nonlinear systems under fuzzy approximation framework is solved by constructing a nonsmooth Lyapunov function and introducing a novel discontinuous controller with dynamic feedback compensator in the design procedure.
Abstract: The problem of asymptotic tracking control for a class of uncertain switched nonlinear systems under fuzzy approximation framework is solved in this paper. Superior to most existing results based on fuzzy adaptive control strategy that can only achieve bounded error tracking performance, our proposed control scheme can guarantee the local asymptotic tracking performance for the uncertain switched nonlinear systems under consideration. This is accomplished by constructing a nonsmooth Lyapunov function and introducing a novel discontinuous controller with dynamic feedback compensator in the design procedure. Meanwhile, some concepts, such as differential inclusion and set-valued map, are introduced to theoretically verify the local asymptotic tracking performance of the systems with our proposed controller. With the help of set-valued Lie derivative, the common virtual control functions, the desired controller, and the adaptive laws can be precisely constructed. Finally, simulation results are given to show the effectiveness of the proposed method.
251 citations
Additional excerpts
...The authors in [13] investigated the output tracking control problem of constrained nonlinear switched systems by using a barrier Lyapunov function (BLF) to prevent system state from violating the constraints....
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TL;DR: It is proved that the overall closed-loop system is stable in the sense of semi-globally uniformly ultimately bounded in mean square, and the output of the switched system converges to a small neighborhood of the origin with appropriate choice of design parameters.
Abstract: This paper considers the problem of adaptive fuzzy backstepping-based output-feedback controller design for a class of uncertain switched nonlinear stochastic systems in lower-triangular form without the measurements of the system states. By combining fuzzy logic systems’ universal approximation ability and dynamic surface control technique in the adaptive backstepping recursive design with a modified average dwell-time scheme, a new adaptive fuzzy control approach is presented for the switched system. More specifically, a switched observer is constructed to reduce the conservativeness aroused by the employ of a common observer, and individual coordinate transformations for subsystems are given up by adopting a common coordinate transformation of all subsystems. It is proved that the overall closed-loop system is stable in the sense of semi-globally uniformly ultimately bounded in mean square, and the output of the switched system converges to a small neighborhood of the origin with appropriate choice of design parameters. Finally, simulation studies are provided to demonstrate the validity of the proposed control method.
195 citations
TL;DR: A framework of adaptive control for a switched nonlinear system with multiple prescribed performance bounds is established using an improved dwell time technique and all signals appearing in the closed-loop system are bounded.
Abstract: In this paper, a framework of adaptive control for a switched nonlinear system with multiple prescribed performance bounds is established using an improved dwell time technique. Since the prescribed performance bounds for subsystems are different from each other, the different coordinate transformations have to be tackled when the system is transformed, which have not been encountered in some switched systems. We deal with the different coordinate transformations by finding a specific relationship between any two different coordinate transformations. To obtain a much less conservative result, in contrast to the common adaptive law, different adaptive laws are established for both active and inactive time-interval of each subsystem. The proposed controllers and switching signals guarantee that all signals appearing in the closed-loop system are bounded. Furthermore, both transient-state and steady-state performances of the switched system are obtained. Finally, the effectiveness of the developed method is verified by the application to a continuous stirred tank reactor system.
195 citations
Cites methods from "Barrier Lyapunov functions for the ..."
...For example, in [46]–[49], the common CT is chosen in the control design procedure by using the backstepping technique....
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References
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01 Jan 1991
TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
Abstract: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
15,545 citations
TL;DR: This review focuses on model predictive control of constrained systems, both linear and nonlinear, and distill from an extensive literature essential principles that ensure stability to present a concise characterization of most of the model predictive controllers that have been proposed in the literature.
8,064 citations
"Barrier Lyapunov functions for the ..." refers background in this paper
...Model Predictive Control that represents an effective control design methodology for handling both constraints and performance issues has been investigated in [9,10]....
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TL;DR: In this paper, the authors survey three basic problems regarding stability and design of switched systems, including stability for arbitrary switching sequences, stability for certain useful classes of switching sequences and construction of stabilizing switching sequences.
Abstract: By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.
3,566 citations
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01 Jan 1990
TL;DR: This book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects, covering a wide range of topics written in a standard theorem/proof style and develops the necessary techniques from scratch.
Abstract: Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.
3,353 citations
TL;DR: Bendixson's theorem is extended to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.
Abstract: We introduce some analysis tools for switched and hybrid systems. We first present work on stability analysis. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability and use iterated function systems theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set. Finally, we extend Bendixson's theorem to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.
3,289 citations