Hybrid Dynamical Systems

Researchers, postgraduate students and professionals in control engineering, applied mathematics and theoretical computer science will find this book presents state-of-the-art concepts, methods, tools and new research for analyzing and describing hybrid dynamical systems. Advanced engineering practitioners and applied researchers working in areas of control engineering, signal processing, communications, and fault detection will find this book an up-to-date resource.

"The book is a self-contained text assuming only a basic mathematical knowledge of modern control theory. It is an excellent up-to-date authoritative reference covering original results with complete mathematical proofs and illustrative examples. The monograph is intended both for researchers and advanced postgraduate students working in the areas of control engineering, theoretical computer science, and applied mathematics interested in the emerging field of hybrid dynamic systems." Zentralblatt Math

Texte du rabat

This book is primarily a research monograph that presents in a unified man ner some recent research on a class of hybrid dynamical systems (HDS). The book is intended both for researchers and advanced postgraduate stu dents working in the areas of control engineering, theoretical computer science, or applied mathematics and with an interest in the emerging field of hybrid dynamical systems. The book assumes competence in the basic mathematical techniques of modern control theory. The material presented in this book derives from a period of fruitful research collaboration between the authors that began in 1994 and is still ongoing. Some of the material contained herein has appeared as isolated results in journal papers and conference proceedings. This work presents this material in an integrated and coherent manner and also presents many new results. Much of the material arose from joint work with students and colleagues, and the authors wish to acknowledge the major contributions made by Ian Petersen, Efstratios Skafidas, Valery Ugrinovskii, David Cook, Iven Mareels, and Bill Moran. There is currently no precise definition of a hybrid dynamical system; however, in broad terms it is a dynamical system that involves a mixture of discrete-valued and continuous-valued variables. Since the early 1990s, a bewildering array of results have appeared under the umbrella of HDS, ranging from the analysis of elementary on-off control systems to sophis ticated mathematical logic-based descriptions of large real-time software systems.

Résumé
This book is primarily a research monograph that presents in a unified man­ ner some recent research on a class of hybrid dynamical systems (HDS). The book is intended both for researchers and advanced postgraduate stu­ dents working in the areas of control engineering, theoretical computer science, or applied mathematics and with an interest in the emerging field of hybrid dynamical systems. The book assumes competence in the basic mathematical techniques of modern control theory. The material presented in this book derives from a period of fruitful research collaboration between the authors that began in 1994 and is still ongoing. Some of the material contained herein has appeared as isolated results in journal papers and conference proceedings. This work presents this material in an integrated and coherent manner and also presents many new results. Much of the material arose from joint work with students and colleagues, and the authors wish to acknowledge the major contributions made by Ian Petersen, Efstratios Skafidas, Valery Ugrinovskii, David Cook, Iven Mareels, and Bill Moran. There is currently no precise definition of a hybrid dynamical system; however, in broad terms it is a dynamical system that involves a mixture of discrete-valued and continuous-valued variables. Since the early 1990s, a bewildering array of results have appeared under the umbrella of HDS, ranging from the analysis of elementary on-off control systems to sophis­ ticated mathematical logic-based descriptions of large real-time software systems.

Contenu
1 Introduction.- 1.1 Hybrid Dynamical Systems.- 1.2 Controller and Sensor Switching Problems.- 1.3 Notation.- 2 Quadratic State Feedback Stabilizability via Controller Switching.- 2.1 Introduction.- 2.2 Quadratic Stabilizability via Asynchronous Controller Switching.- 2.3 The S-Procedure.- 2.4 A Sufficient Condition for Quadratic Stabilizability.- 2.5 The Case of Two Basic Controllers.- 2.6 Quadratic Stabilizability via Synchronous Switching.- 2.7 Illustrative Example.- 2.8 Proof of Theorem 2.3.1.- 3 Robust State Feedback Stabilizability with a Quadratic Storage Function and Controller Switching.- 3.1 Introduction.- 3.2 Uncertain Systems with Norm-Bounded Uncertainty.- 3.3 Robust Stabilizability via Asynchronous Controller Switching.- 3.4 Robust Stabilizability via Synchronous Switching.- 3.5 Illustrative Examples.- 4 H? Control with Synchronous Controller Switching.- 4.1 Introduction.- 4.2 State Feedback H? Control Problem.- 4.3 Output Feedback H? Control Problem.- 4.4 Illustrative Example.- 4.5 Output Feedback H? Control over Infinite Time.- 5 Absolute Stabilizability via Synchronous Controller Switching.- 5.1 Introduction.- 5.2 Uncertain Systems with Integral Quadratic Constraints.- 5.3 State Feedback Stabilizability via Synchronous Controller Switching.- 5.4 Output Feedback Stabilizability via Synchronous Controller Switching.- 5.5 A Necessary and Sufficient Condition for Output Feedback Stabilizability.- 5.6 A Constructive Method for Output Feedback Absolute Stabilization.- 5.7 Systems with Structured Uncertainty.- 5.8 Illustrative Example.- 6. Robust Output Feedback Controllability via Synchronous Controller Switching.- 6.1 Introduction.- 6.2 Robust Output Feedback Controllability.- 6.3 A Necessary and Sufficient Condition for Robust Controllability.- 7Optimal Robust State Estimation via Sensor Switching.- 7.1 Introduction.- 7.2 Robust Observability of Uncertain Linear Systems.- 7.3 Optimal Robust Sensor Scheduling.- 7.4 Model Predictive Sensor Scheduling.- 8 Almost Optimal Linear Quadratic Control Using Stable Switched Controllers.- 8.1 Introduction.- 8.2 Optimal Control via Stable Output Feedback Controllers.- 8.3 Construction of Almost Optimal Stable Switched Controller.- 9 Simultaneous Strong Stabilization of Linear Time-Varying Systems Using Switched Controllers.- 9.1 Introduction.- 9.2 The Problem of Simultaneous Strong Stabilization.- 9.3 A Method for Simultaneous Strong Stabilization.- References.