Hybrid Dynamical Systems : Controller and Sensor Switching Problems

The area of hybrid dynamical systems (HDS) represents a difficult and exciting challenge to control engineers and is referred to as "the control theory of tomorrow" because of its future potential for solving problems. This relatively new discipline bridges control engineering, mathematics, and computer science. There is now an emerging literature on this topic describing a number of mathematical models, heuristic algorithms, and stability criteria. However, presently there is no systematic theory of HDS. "Hybrid Dynamical Systems" focuses on a comprehensive development of HDS theory and integrates results established by the authors. The work is a self-contained informative text/reference, covering several theoretically interesting and practically significant problems concerning the use of switched controllers and examining the sensor scheduling problem. The emphasis is on classes of uncertain systems as models for HDS. Features and topics: * Focuses on the design of robust HDS in a logical and clear manner * Applies the hybrid control systems framework to two classical robust control problems: design of an optimal stable controller for a linear system and simultaneous stabilization of a collection of plants * Presents a detailed treatment of stability and H-infinity control problems for a class of HDS * Covers recent original results with complete mathematically rigorous proofs Researchers and postgraduate students in control engineering, applied mathematics, and theoretical computer science will find this book covers the latest results on this important area of research. 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. Cover ......Page 1 Title Page ......Page 3 Contents......Page 5 Preface......Page 9 1.1 Hybrid Dynamical Systems......Page 11 1.2.1 Switched Dynamical Systems......Page 13 1.2.3 Robust Switched Controller Systems......Page 15 1.2.4 Switched Sensor Systems......Page 16 1.3 Notation......Page 17 2.1 Introduction......Page 21 2.2 Quadratic Stabilizability via Asynchronous Controller Switching......Page 22 2.2.1 Asynchronous Quadratic Stabilizability of Linear Systems......Page 24 2.3 The S-Procedure......Page 26 2.3.1 An S-Procedure Result for Two Quadratic Forms......Page 27 2.3.2 The S- Procedure and Completeness......Page 28 2.4 A Sufficient Condition for Quadratic Stabilizability......Page 29 2.5 The Case of Two Basic Controllers......Page 30 Synchronous Controller Switching......Page 31 2.6.1 A Sufficient Condition for Quadratic Stabilizability via Synchronous Controller Switching......Page 34 2.7 Illustrative Example......Page 35 2.8 Proof of Theorem 2.3.1......Page 37 3.1 Introduction......Page 43 3.2 Uncertain Systems with Norm-Bounded Uncertainty......Page 44 3.2.1 Special Case: Sector-Bounded Nonlinearities......Page 45 3.3 Robust Stabilizability via Asynchronous Controller Switching......Page 46 3.3.1 Sufficient Conditions for Robust Stabilizability via Asynchronous Controller Switching......Page 50 3.4 Robust Stabilizability via Synchronous Switching......Page 51 3.4.1 Sufficient Conditions for Robust Stabilizability via Synchronous Controller Switching......Page 55 3.5.1 A Second-Order System......Page 56 3.5.2 Two-Mass Spring System......Page 59 4.1 Introduction......Page 65 4.2 State Feedback H-inf Control Problem......Page 66 4.3 Output Feedback H-inf Control Problem......Page 68 4.3.1 The Case of Linear Static Basic Controllers......Page 74 4.4 Illustrative Example......Page 76 4.5 Output Feedback H-inf Control over Infinite Time......Page 78 4.5.1 Construction of an Infinite-Time Output Feedback H-inf Controller......Page 79 5.1 Introduction......Page 85 5.2 Uncertain Systems with Integral Quadratic Constraints......Page 86 5.3 State Feedback Stabilizability via Synchronous Controller Switching......Page 90 5.4 Output Feedback Stabilizability via Synchronous Controller Switching......Page 92 5.5 A Necessary and Sufficient Condition for Output Feedback Stabilizability......Page 94 5.6 A Constructive Method for Output Feedback Absolute Stabilization......Page 97 5.7 Systems with Structured Uncertainty......Page 99 5.8 Illustrative Example......Page 103 6.1 Introduction......Page 107 6.2 Robust Output Feedback Controllability......Page 108 6.3 A Necessary and Sufficient Condition for Robust Controllability......Page 110 7.1 Introdliction......Page 117 7.2 Robust Observability of Uncertain Linear Systems......Page 119 7.3 Optimal Robust Sensor Scheduling......Page 123 7.4 Model Predictive Sensor Scheduling......Page 128 8.1 Introduction......Page 131 8.2 Optimal Control via Stable Output Feedback Controllers......Page 132 8.3 Construction of Almost Optimal Stable Switched Controller......Page 134 9.1 Introduction......Page 139 9.2 The Problem of Simultaneous Strong Stabilization......Page 140 9.3 A Method for Simultaneous Strong Stabilization......Page 141 References......Page 147 Index ......Page 161 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. The term "hybrid dynamical system" (HDS) has many meanings, the most common of which is a dynamical system that involves the interaction of discrete and continuous dynamics.