Stability and Control of Dynamical Systems with Applications: A Tribute to Anthony N. Michel

458 Pages·2003·16.99 MB·English

by  Alfred Fettweis (auth.)

Control Engineering
Series Editor
WilliamS. Levine
Department of Electrical and Computer Engineering
University of Maryland
College Park, MD 20742-3285
USA
Editorial Advisory Board
Okko Bosgra William Powers
Delft University Ford Motor Company (retired)
The Netherlands USA
Graham Goodwin Mark Spong
University of Newcastle University of Illinois
Australia Urbana-Champaign
USA
Petar Kokotovic
University of California lori Hashimoto
Santa Barbara Kyoto University
USA Kyoto, Japan
Manfred Morari
ETH
Zürich, Switzerland
Stability and Control
of Dynamical Systems
with Applications
A Tribute to Anthony N. Michel
Derong Liu
Panos J. Antsaklis
Editors
Springer Science+Business Media, LLC
Derong Liu Panos J. Antsaklis
University of Illinois at Chicago University of Notre Dame
Department of Electrical Department of Electrical Engineering
and Computer Engineering Notre Dame, IN 46556
Chicago, Illinois 60607 USA
USA
Library of Congress Cataloging-in-Publication Data
Stability and control of dynamical systems with applications : a tribuet to Anthony N.
Michel / Derong Liu, Panos J. Antsaklis, editors,
p. cm.
Selected papers presented at the workshop at the University of Notre Dame on Apr. 5,2003.
Includes bibliographical references and index.
ISBN 978-1-4612-6583-2 ISBN 978-1-4612-0037-6 (eBook)
DOI 10.1007/978-1-4612-0037-6
1. Stability-Congresses. 2. Differentiable dynamical systems-Congresses. 3. Control
theory—Congresses. I. Michel, Anthony N. II. Liu, Derong, 1963- III. Antsaklis, Panos J.
QA871.S7634 2004
003\5-dc21
2003045390
CIP
Printed on acid-free paper.
© 2003 Springer Science+Business Media New York
Originally published by Birkhäuser Boston in 2003
Softcover reprint of the hardcover 1st edition 2003
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer Science+Business Media, LLC), except for brief excerpts in
connection with reviews or scholarly analysis. Use in connection with any form of information storage
and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now
known or hereafter developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former
are not especially identified, is not to be taken as a sign that such names, as understood by the Trade
Marks and Merchandise Marks Act, may accordingly be used freely by anyone.
ISBN 978-1-4612-6583-2 SPIN 10952331
Typeset by the editors.
9 8 7 6 5 4 3 21
To Anthony N. Michel
Anthony N. Michel
Contents
Foreword xiii
Preface xv
Anthony N. Michel: A Friend, a Scholar, and a Mentor
D. Liu and P. J. Antsaklis xix
Summary of Research Accomplishments of Anthony N. Michel. xx
Theses Supervised by Anthony N. Michel xxii
Bibliography ............... xxiv
List of Contributors xxvii
PART I: ISSUES IN STABILITY ANALYSIS
1 Wave-Digital Concepts and Relativity Theory
A. Fettweis 3
1.1 Introduction . . . . . . . . . . . . . . . . . 4
1.2 Nonlinear Passive Kirchhoff Circuits and the Wave-Digital Method. 5
1.3 Nonlinear Relativistic Mass. . . . . . . . . 6
1.4 Direct Derivation of the Alternative Results 9
1.5 Some Applications 17
1.6 Conclusions 19
Bibliography ...... 21
2 Time, Systems, and Control: Qualitative Properties and Methods
L. T. Gruyitch 23
2.1 Introduction......... . ...... 24
2.2 Physical Variables, Time, and Continuity . 24
2.3 Complete Transfer Function Matrix ... 26
2.4 Consistent Lyapunov Methodology for Nonlinear Systems 30
2.5 Vector Lyapunov Function Concept and Complex Systems 33
vii
viii Contents
2.6 Conclusions 37
2.7 Appendix 38
Bibliography .. 41
3 Asymptotic Stability of Multibody Attitude Systems
J. Shen, A. K. Sanyal, and N. H. McClamroch 47
3.1 Introduction................... 47
3.2 Equations of Motion ............. . 48
3.3 Conservation of Energy and Lyapunov Stability 50
3.4 Asymptotic Stability Analysis 51
3.5 Examples . 63
3.6 Conclusions 69
Bibliography .. 70
4 Robust Regulation of Poly topic Uncertain Linear Hybrid Systems with
Networked Control System Applications
H. Lin and P. 1. Antsaklis 71
4.1 Introduction............ 72
4.2 Problem Formulation . . . . . . . 74
4.3 Robust One-Step Predecessor Set. 76
4.4 Safety, Reachability, and Attainability 81
4.5 Hybrid Regulation ......... 82
4.6 Networked Control Systems (NCS) . 88
4.7 Conclusions 93
Bibliography ............... 95
5 Stability Analysis of Swarms in a Noisy Environment
K. M. Passino 97
5.1 Introduction.................... 97
5.2 Swarm and Environment Models . . . . . . . . . 98
5.3 Stability Analysis of Swarm Cohesion Properties 102
5.4 Cohesion Characteristics and Swarm Dynamics 111
5.5 Conclusions 115
Bibliography ...................... 115
6 Stability of Discrete Time-Varying Linear Delay Systems and
Applications to Network Control
M. L. Sichitiu and P. H. Bauer 117
6.1 Introduction... 117
6.2 The Stability Test . . . . 118
6.3 The Algorithm ..... 122
6.4 Applications in Communication Network Control 124
Contents ix
6.5 Conclusions......................... 128
6.6 Appendix: Pseudocode for the Stability Testing Algorithm 129
Bibliography ........................... 129
7 Stability and £2 Gain Analysis of Switched Symmetric Systems
G. Zhai 131
7.1 Introduction and Problem Formulation . 131
7.2 Stability Analysis 135
7.3 £2 Gain Analysis 140
7.4 Conclusions 150
Bibliography ..... 150
PART II: NEURAL NETWORKS AND SIGNAL PROCESSING
8 Approximation of Input-Output Maps using Gaussian Radial Basis
Functions
I. W Sandberg 155
8.1 Introduction........................... 155
8.2 Preliminaries ... . . . . . . . . . . . . . . . . . . . . . . . 157
8.3 Radial Basis Function Approximations of Input-Output Maps. 158
8.4 An Example . . . . . . . . . . . 161
8.5 Related Results and Comments . 163
Bibliography ............ . 165
9 Blind Source Recovery: A State-Space Formulation
K. Waheed and F. M. Salem 167
9.1 Introduction............ 167
9.2 Optimization Framework for BSR 171
9.3 Extensions to the Natural Gradient 176
9.4 Simulation Results ....... . 181
9.5 Conclusions ........... . 188
9.6 Appendix: MIMO Canonical Form. 188
Bibliography ............. . 189
10 Direct Neural Dynamic Programming
L. Yang, R. Enns, Y. T. Wang, and 1. Si 193
10.1 Introduction . . . . . . . . . . . . 193
10.2 ADP Models and Algorithms ... 194
10.3 Direct Neural Dynamic Programming (NDP) 199
10.4 A Control Problem: Helicopter Command Tracking . 204
10.5 Conclusions 213
Bibliography ....................... . 213
x Contents
11 Online Approximation-Based Aircraft State Estimation
1. Farrell, M. Sharma, and M. Polycarpou 215
11.1 Introduction . . . . . . . . . . . . . . . 215
11.2 Aircraft Dynamics and Model Structure 217
11.3 Approximator Definition . . . . . . . . 219
11.4 On-Line Approximation-Based Estimation. 222
11.5 Prediction Error-Based Learning . . . 224
11.6 Lyapunov Analysis: Prediction Error . 224
11.7 Implementation Issues .. . 226
11.8 Conclusions ........ . 228
11.9 Appendix: Aircraft Notation 229
Bibliography .......... . 230
12 Evolutionary Multiobjective Optimization: Qualitative Analysis and
Design Implementation
G. G. Yen 233
12.1 Introduction . . . . 234
12.2 Evolutionary Multiobjective Optimization Algorithms .... 235
12.3 Dynamic Multiobjective Evolutionary Algorithm (DMOEA) 238
12.4 Comparative Study 248
12.5 Robustness Study 251
12.6 Conclusions 252
Bibliography ..... 252
13 Set-Membership Adaptive Filtering
Y. F Huang 255
13.1 Introduction . . . . . . . . . . . 255
13.2 Problem Formulation ............. . 256
13.3 Optimal Bounding Ellipsoid (OBE) Algorithms 258
13.4 Set-Membership NLMS (SM-NLMS) Algorithm 263
13.5 Conclusions 264
Bibliography ..................... . 264
PART III: POWER SYSTEMS AND CONTROL SYSTEMS
14 Trajectory Sensitivity Theory in Nonlinear Dynamical Systems: Some
Power System Applications
M. A. Pai and T. B. Nguyen 271
14.1 Introduction. . . . . . . . . . . . . . . . . . 271
14.2 Trajectory Sensitivity Analysis (TSA) . . . . 274
14.3 Trajectory Sensitivity Theory for DAE Model 274
14.4 Stability-Constrained Optimal Power Flow Formulation. 283