Hybrid Dynamical Systems

by Savkin, Andrey V.; Evans, Robin J.

• ISBN13: 9780817642242
• ISBN10: 0817642242
• Format: Hardcover
• Copyright: 2002-07-01
• Publisher: Birkhauser

Summary

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.

Table of Contents

Preface	ix
Introduction	1	(10)
Hybrid Dynamical Systems	1	(2)
Controller and Sensor Switching Problems	3	(4)
Switched Dynamical Systems	3	(1)
Switched Controller Systems	4	(1)
Robust Switched Controller Systems	5	(1)
Switched Sensor Systems	6	(1)
Switched Controllers for Strong Stabilization of Linear Systems	7	(1)
Notation	7	(4)
Quadratic State Feedback Stabilizability via Controller Switching	11	(22)
Introduction	11	(1)
Quadratic Stabilizability via Asynchronous Controller Switching	12	(4)
Asynchronous Quadratic Stabilizability of Linear Systems	14	(2)
The S-Procedure	16	(3)
An S-Procedure Result for Two Quadratic Forms	17	(1)
The S-Procedure and Completeness	18	(1)
A Sufficient Condition for Quadratic Stabilizability	19	(1)
The Case of Two Basic Controllers	20	(1)
Quadratic Stabilizability via Synchronous Switching	21	(4)
A Sufficient Condition for Quadratic Stabilizability via Synchronous Controller Switching	24	(1)
Stabilization via Synchronous Switching with Two Basic Controllers	25	(1)
Illustrative Example	25	(2)
Proof of Theorem 2.3.1	27	(6)
Robust State Feedback Stabilizability with a Quadratic Storage Function and Controller Switching	33	(22)
Introduction	33	(1)
Uncertain Systems with Norm-Bounded Uncertainty	34	(2)
Special Case: Sector-Bounded Nonlinearities	35	(1)
Robust Stabilizability via Asynchronous Controller Switching	36	(5)
Sufficient Conditions for Robust Stabilizability via Asynchronous Controller Switching	40	(1)
Robust Stabilizability via Synchronous Switching	41	(5)
Sufficient Conditions for Robust Stabilizability via Synchronous Controller Switching	45	(1)
Illustrative Examples	46	(9)
A Second-Order System	46	(3)
Two-Mass Spring System	49	(6)
H∞ Control with Synchronous Controller Switching	55	(20)
Introduction	55	(1)
State Feedback H∞ Control Problem	56	(2)
Output Feedback H∞ Control Problem	58	(8)
The Case of Linear Static Basic Controllers	64	(2)
Illustrative Example	66	(2)
Output Feedback H∞ Control over Infinite Time	68	(7)
Construction of an Infinite-Time Output Feedback H∞ Controller	69	(6)
Absolute Stabilizability via Synchronous Controller Switching	75	(22)
Introduction	75	(1)
Uncertain Systems with Integral Quadratic Constraints	76	(4)
State Feedback Stabilizability via Synchronous Controller Switching	80	(2)
Output Feedback Stabilizability via Synchronous Controller Switching	82	(2)
A Necessary and Sufficient Condition for Output Feedback Stabilizability	84	(3)
A Constructive Method for Output Feedback Absolute Stabilization	87	(2)
Systems with Structured Uncertainty	89	(4)
Illustrative Example	93	(4)
Robust Output Feedback Controllability via Synchronous Controller Switching	97	(10)
Introduction	97	(1)
Robust Output Feedback Controllability	98	(2)
A Necessary and Sufficient Condition for Robust Controllability	100	(7)
Optimal Robust State Estimation via Sensor Switching	107	(14)
Introduction	107	(2)
Robust Observability of Uncertain Linear Systems	109	(4)
Optimal Robust Sensor Scheduling	113	(5)
Model Predictive Sensor Scheduling	118	(3)
Almost Optimal Linear Quadratic Control Using Stable Switched Controllers	121	(8)
Introduction	121	(1)
Optimal Control via Stable Output Feedback Controllers	122	(2)
Construction of Almost Optimal Stable Switched Controller	124	(5)
Simultaneous Strong Stabilization of Linear Time-Varying Systems Using Switched Controllers	129	(8)
Introduction	129	(1)
The Problem of Simultaneous Strong Stabilization	130	(1)
A Method for Simultaneous Strong Stabilization	131	(6)
References	137	(14)
Index	151