Book•
Switching in Systems and Control
24 Jun 2003-
TL;DR: I. Stability under Arbitrary Switching, Systems not Stabilizable by Continuous Feedback, and Systems with Sensor or Actuator Constraints with Large Modeling Uncertainty.
Abstract: I. INTRODUCTION 1. Basic Concepts II . STABILITY OF SWITCHED SYSTEMS 2. Stability under Arbitrary Switching 3. Stability under Constrained Switching III. SWITCHING CONTROL 4. Systems not Stabilizable by Continuous Feedback 5. Systems with Sensor or Actuator Constraints 6. Systems with Large Modeling Uncertainty IV. SUPPLEMENTARY MATERIAL A. Stability B. Lie Algebras Notes and References Bibliography Index
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01 Jan 2006
TL;DR: This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms, into planning under differential constraints that arise when automating the motions of virtually any mechanical system.
Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.
6,340 citations
Cites background from "Switching in Systems and Control"
...Most of this work considers how to design control laws for piecewise-smooth systems [139, 637]....
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...For discussions of piecewise-smooth vector fields, see [27, 637, 848, 998]....
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...Such differential equations model hybrid systems in control theory [139, 411, 637]....
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TL;DR: This paper focuses on the stability analysis for switched linear systems under arbitrary switching, and highlights necessary and sufficient conditions for asymptotic stability.
Abstract: During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.
2,470 citations
Cites background from "Switching in Systems and Control"
...refer to [47], [48], [58] for further details on the Lie algebraic conditions....
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...There have been several excellent survey papers on the stability of switched systems; see for example the survey papers [22], [34], [49], [61], the recent books [43], [47] and the references cited therein....
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...Recent efforts in switched linear system research typically focus on the analysis of dynamic behaviors, such as stability [22], [34], [43], [47], [49], controllability, reachability [16], [41], [42], [85], [86] and observability [4], [24], [36] etc....
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...There are examples [47] (Chapter 2) of systems that do not have a CQLF, but are exponentially stable under arbitrary switching....
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TL;DR: In this paper, the authors present a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems and on the basics of hybrid control, focusing on the robustness of asymptotic stability to data perturbation, external disturbances and measurement error.
Abstract: Robust stability and control for systems that combine continuous-time and discrete-time dynamics. This article is a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems, and on the basics of hybrid control. The presentation and selection of material is oriented toward the analysis of asymptotic stability in hybrid systems and the design of stabilizing hybrid controllers. Our emphasis on the robustness of asymptotic stability to data perturbation, external disturbances, and measurement error distinguishes the approach taken here from other approaches to hybrid systems. While we make some connections to alternative approaches, this article does not aspire to be a survey of the hybrid system literature, which is vast and multifaceted.
1,773 citations
Cites background or methods from "Switching in Systems and Control"
...For example, parameterization by t [ R$0 is used for switched systems [49] as well as for impulsive dynamical systems [43], [30]....
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...” The algorithm for defining generalized solutions in “Robustness and Switching Systems A switching system is a differential equation whose right-hand side is chosen from a family of functions based on a switching signal [49], [S4]....
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Book•
27 Jul 2017TL;DR: Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.
Abstract: Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.
1,142 citations
Cites background from "Switching in Systems and Control"
...The reader is also referred to the book by Liberzon [191]....
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TL;DR: In this paper, the authors present an introductory tutorial on discontinuous dynamical systems, and present non-smooth stability tools to characterize the asymptotic behavior of solutions.
Abstract: This article has presented an introductory tutorial on discontinuous dynamical systems. Various examples illustrate the pertinence of the continuity and Lipschitzness properties that guarantee the existence and uniqueness of classical solutions to ordinary differential equations. The lack of these properties in examples drawn from various disciplines motivates the need for more general notions than the classical one. First, we introduced notions of solution for discontinuous systems. Second, we reviewed the available tools from non- smooth analysis to study the gradient information of candidate Lyapunov functions. And, third, we presented nonsmooth stability tools to characterize the asymptotic behavior of solutions.
1,022 citations