Stable Adaptive Neural Network Control

295 Pages·2002·15.55 MB·English

by  Shuzhi S. Ge

STABLE ADAPTIVE NEURAL
NETWORK CONTROL
The Kluwer International Series on
ASIAN STUDIES IN COMPUTER
AND INFORMATION SCIENCE
Series Editor
Kai-Yuan Cai
Beijing University ofA eronautics and Astronautics, Beijing, CHINA
Editorial Advisory Board
Han-Fu Chen, Institute of System Science, Chinese Academy of Sciences
Jun-Liang Chen, Beijing University of Post and Telecommunication
Lin Huang, Peking University
Wei Li, Beijing University of Aeronautics and Astronautics
Hui-Min Lin, Institute of Software Technology, Chinese Academy of Sciences
Zhi-Yong Liu, Institute of Computing Technology, Chinese Academy of Sciences
Ru-Qian Lu, Institute of Mathematics, Chinese Academy of Sciences
Shi-Tuan Shen, Beijing University of Aeronautics and Astronautics
Qing-Yun Shi, Peking University
You-Xian Sun, Zhejiang University
Lian-Hua Xiao, National Natural Science Foundation of China
Xiao-Hu You, Southeast University
Bo Zhang, Tsinghua University
Da-Zhong Zheng, Tsinghua University
Bing-Kun Zhou, Tsinghua University
Xing-Ming Zhou, Changsha University of Technology
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STABLE ADAPTIVE NEURAL
NETWORK CONTROL
by
S. S. Ge
C. C. Hang
T. H. Lee
T. Zhang
0/
Department Electrical Engineering
National University a/Singapore
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
Stable adaptive neural network control/by S. S. Ge ... ret al.J.
p. cm.--(The Kluwer international series on Asian studies in computer and
information science; 13)
Includes bibliographical references and index.
ISBN 978-1-4419-4932-5 ISBN 978-1-4757-6577-9 (eBook)
DOI 10.1007/978-1-4757-6577-9
1. Adaptive control systems. 2. Neural networks (Computer science) 1. Ge, S.S.
(Shuzhi S.) II. Series.
TJ217.S7362001
629.8'3--dc21 2001050337
Copyright © 2002 by Springer Science+Business· Media New York
Originally published by Kluwer Academic Publishers in 2002
Softcover reprint of the hardcover 1s t edition 2002
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system
or transmitted in any form or by any means, mechanical, photo-copying, recording, or otherwise,
without the prior written permission of the publisher, Springer Science+Business Media, LLC.
Printed on acidjree paper.
To
Jinlan, Sao Chin, Ruth, Yuan
and
our loved ones
SERIES EDITOR'S
ACKNOWLEDGMENTS
I am pleased to acknowledge the assistance to the editorial work by
Beijing University of Aeronautics and Astronautics and the National
Natural Science Foundation of China
Kai-Yuan Cai
Series Editor
Department ofA utomatic Control
Beijing University ofA eronautics and Astronautics
Beijing 100083
China
I do not know what I may appear to the world, bu.t to myself I seem to have
been only like a boy playing on the seashore, diverting myself in now and then
finding a smoother pebble or a prettier shell than ordinary, while the great ocean
of truth lay all u.ndiscovered before me.
-Isaac Newton
Contents
Preface xiii
1 Introduction 1
1.1 Introduction . 1
1.2 Adaptive Control . 2
1.3 Neural Network Control 3
1.4 Instability Mechanisms in Adaptive Neural Control Systems .5
1.5 Outline of the Book 9
1.6 Conclusion 10
2 Mathematical Preliminaries 11
2.1 Introduction . 11
2.2 Mathematical Preliminaries 11
2.2.1 Norms for Vectors and Signals 12
2.2.2 Properties of Matrix 15
2.3 Concepts of Stability . 16
2.4 Lyapunov Stability Theorem 17
2 ..5 Useful Theorems and Formula. 19
2.5.1 Sliding Surface 19
2 ..5 .2 Mean Value Theorem 20
2.5.3 Integral Formula 20
2.5.4 Implicit Function Theorem 23
2.5.5 Input-Output Stability . 25
2.6 Conclusion 26
3 Neural Networks and Function Approximation 27
3.1 Introduction. 27
3.2 Function Approximation . 27
3.3 Linearly Parametrized Neural Networks 29
3.4 Non-linearly Parametrized Networks 35
3.5 Neural Networks for Control Applications 44
3.6 Conclusion 46
x Contents
4 SISO Nonlinear Systems 47
4.1 Introduction.............. 47
4.2 NN Control with Regional Stability. 49
4.2.1 Desired Feedback Control . . 49
4.2.2 HONN Controller Design Based on (4.7) . 51
4.2.3 MNN Control Based on (4.10) ...... 59
4.3 VSC - Semi-Global Stability .......... 70
4.3.1 VSC-based Adaptive NN Control Design. 73
4.3.2 Elimination for Controller Chattering 77
4.3.3 Simulation Study. 79
4.4 Conclusion ....... 79
5 ILF for Adaptive Control 81
5.1 Introduction............. 81
5.2 Matching SISO Nonlinear Systems 82
5.2.1 Integral Lyapunov Function 83
5.2.2 Choice of Weighting Function Q(x) 83
5.2.3 Adaptive NN Control Based on DFCs 92
.5.3 Backstepping Adaptive NN Design . . . . . . 10.5
.5.3.1 Adaptive Design for a First-order System 108
.5.3.2 Design for nth-order Systems . . . . . . . 112
.5.3.3 Controller Design with Reduced Knowledge 121
5.3.4 Simulation Studies . . . . . . . . . 123
.5.4 NN Control for MIMO Nonlinear Systems . . . . . 127
5.4.1 System Description. . . . . . . . . . . . . . 128
5.4.2 Lyapunov Function Design and Control Structure 130
.5.4.3 Adaptive MIMO Control Using MNNs 132
.5.5 Conclusion .......................... 138
6 Non-affine Nonlinear Systems 139
6.1 Introduction................. 139
6.2 System Description and Properties . . . . 140
6.2.1 Implicit Desired Feedback Control 142
6.2.2 High-gain Observer. . . . . 146
6.3 Controller Design Based on LPNN 147
6.3.1 State Feedback Control . 149
6.3.2 Output Feedback Control . 153
6.3.3 Simulation Study. . . . . . 159
6.4 Controller Design Based on MNN . 160
6.4.1 State Feedback Control . 163
6.4.2 Output Feedback Control 168
6.4.3 Application to CSTR .. 176
Contents xi
6.5 Conclusion ......... . 182
7 Triangular Nonlinear Systems 183
7.1 Introduction................. 183
7.2 Special Systems in Strict-Feedback Form. 185
7.2.1 Direct Adaptive NN Control 188
7.2.2 Simulation studies ....... . 198
7.3 Partially Known Nonlinear Systems .. 201
7.3.1 Adaptive Neural Control Design 203
7.3.2 Numerical Simulation ..... . 215
7.4 Pure-feedback Nonlinear Systems ... . 217
7.4.1 Direct Adaptive NN Control for El . 220
7.4.2 Direct Adaptive NN Control for E2 . 235
7.4.3 Simulation studies 240
7.5 MIMO Nonlinear Systems 242
7.6 Conclusion ....... . 260
8 Conclusion 261
8.1 Conclusion 261
8.2 Design Flexibility . 262
8.3 Further Research 263
References 265
Index 281