Table Of ContentCommunications and Control Engineering
Springer-Verlag London Ltd.
Published titles include:
Constructive Nonlinear Control
R. Sepulchre, M. Jankovic and P.V. Kokotovic
A Theory ofL earning and Generalization
M. Vidyasagar
Adaptive Control
I.D. Landau, R. Lozano and M.M' Saad
Stabilization ofN onlinear Uncertain Systems
Miroslav Krstic and Hua Deng
Passivity-based Control ofE uler-Lagrange Systems
Romeo Ortega, Antonio Loria, Per Johan Nicklasson and Hebertt Sira-Ramirez
Stability and Stabilization ofI nfinite Dimensional Systems with Applications
Zheng-Hua Luo, Bao-Zhu Guo and Orner Morgul
Nonsmooth Mechanics (2nd edition)
Bernard Brogliato
Nonlinear Control Systems II
Alberto Isidori
LrGain and Passivity Techniques in nonlinear Control
Arjan van der Schaft
Control ofL inear Systems with Regulation and Input Constraints
Ali Saberi, Anton A. Stoorvogel and Peddapullaiah Sannuti
Robust and Hoo Control
BenM. Chen
Computer Controlled Systems
Efim N. Rosenwasser and Bernhard P. Lampe
Dissipative Systems Analysis and Control
Rogelio Lozano, Bernard Brogliato, Olav Egeland and Bernhard Maschke
Control ofC omplex and Uncertain Systems
Stanislav V. Emelyanov and Sergey K. Korovin
Robust Control Design Using H'" Methods
Ian R.Petersen, Valery A. Ugrinovski and Andrey V.Savkin
Model Reduction for Control System Design
Goro Obinata and Brian D. O. Anderson
Control Theory for Linear Systems
Harry L. Trentelman, Anton Stoorvogel and Malo Hautus
Simon G. Fabri and Visakan Kadirkamanathan
Functional Adaptive
Control
An Intelligent Systems Approach
With 74 Figures
i
Springer
Simon G. Fabri, PhD
Department of Electrical Power and Control Engineering, University of Malta,
Msida MSD 06, Malta
Visakan Kadirkamanathan, PhD
Department of Automatic Control and Systems Engineering,
The U niversity of Sheffield, Sheffield, SI 3J D
Series Editors
E.D. Sontag • M. Thoma
ISSN 0178-5354
ISBN 978-1-4471-1090-3 ISBN 978-1-4471-0319-6 (eBook)
DOI 10.1007/978-1-4471-0319-6
British Library Cataloguing in Publication Data
Fabri, Simon G.
Functional adaptive control : an intelligent systems
Approach. -(communications and control engineering)
1. Adaptive control systems 2. Intelligent control systems
1. Title II. Kadirkamanathan, Visakan
629.8
ISBN 9781447110903
Library of Congress Cataloging-in-Publication Data
Fabri, Simon G., 1965-
Functional adaptive control : an intelligent systems approach. .Simon
G. Fabri and Visakan Kadirkamanathan.
p. cm. --(Communications and control engineering)
Includes bibliographical references and index.
ISBN 978-1-4471-1090-3 (alk. paper)
1. Adaptive control systems. 2. Intelligent control systems. 1.
Kadirkamanathan, Visakan, 1962- II. Title. III. Series.
TJ217 .F33 2001
629.8' 36-dc21
2001016083
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
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publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued
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sent to the publishers.
© Springer-V eriag London 200 I
Originally published by Springer-Verlag London Berlin Heidelberg in 2001
Softcover reprint of the hardcover Ist edition 2001
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a
specific statement, that such names are exempt from the relevant laws and regulations and therefore
free for general use.
The publisher makes no representation, express or implied, with regard to the accuracy of the
information contained in this book and cannot accept any legal responsibility or liability for any errors
or omissions that may be made.
Typesetting: Camera ready by authors
69/3830-543210 Printed on acid-free paper SPIN 10779960
To Miriam, Gemima and Jean-Marc (S.F)
To my mother (V.K)
Preface
The field of intelligent control has recently emerged as a response to the
challenge of controlling highly complex and uncertain nonlinear systems. It
attempts to endow the controller with the key properties of adaptation, learn
ing and autonomy. The field is still immature and there exists a wide scope
for the development of new methods that enhance the key properties of in
telligent systems and improve the performance in the face of increasingly
complex or uncertain conditions.
The work reported in this book represents a step in this direction. A num
ber of original neural network-based adaptive control designs are introduced
for dealing with plants characterized by unknown functions, nonlinearity,
multimodal behaviour, randomness and disturbances. The proposed schemes
achieve high levels of performance by enhancing the controller's capability
for adaptation, stabilization, management of uncertainty, and learning. Both
deterministic and stochastic plants are considered.
In the deterministic case, implementation, stability and convergence is
sues are addressed from the perspective of Lyapunov theory. When compared
with other schemes, the methods presented lead to more efficient use of com
putational storage and improved adaptation for continuous-time systems, and
more global stability results with less prior knowledge in discrete-time sys
tems.
Stochastic systems are handled by using concepts from stochastic adaptive
optimal control, leading to novel dual adaptive control schemes that take
into consideration the extent of the uncertainty when generating the control
signal. This yields a highly improved transient response, particularly in the
absence of prior network training. Multiple model techniques are used to
address the complexity arising from multimodal behaviour. These lead to
a reconfigurable control scheme for uncertain jump-nonlinear systems, and
also an adaptive form of gain scheduling for plants characterized by unknown
complex nonlinearities.
A range of simulation experiments are included, confirming that these
novel designs are truly effective for dealing with the stringent conditions
usually associated with intelligent control.
November 2000 Simon G. Fabri and Visakan K adirkamanathan
Acknowledgements
The book arose out of the first author's research towards his degree of Ph.D.
at the Department of Automatic Control & Systems Engineering, University
of Sheffield, United Kingdom, under the supervision of the second author.
During the period of three years from 1996 - 1999, we have had numerous
interesting conversations on various aspects of control and estimation and
have been a source of inspiration to each other.
The first author's Ph.D. research programme was financially supported
by a CVCP Overseas Research Students (ORS) award of the U.K., a staff
development scholarship from the University of Malta and funds from the
Department of Automatic Control & Systems Engineering of the University
of Sheffield. These funds were made possible by the support of Professor
Joseph A. Agius of the University of Malta and Professor Peter J. Fleming
of The University of Sheffield. The second author acknowledges the support
of his academic colleagues who have had to share the teaching load and the
support of the University of Sheffield which granted a study leave to enable
this book to be written.
A very special thank you goes to our wives Miriam and Manjula for their
interest, encouragement, patience and moral support during these particu
larly busy years. Thanks also to our parents and siblings who have always
been an example to follow.
Finally we would like to thank the ACSE Department's general office and
programming staff for secretarial and technical assistance. We also acknowl
edge all those who helped indirectly, perhaps by a word of encouragement or
a sincere expression of interest. In particular we would like to mention our
colleagues Mr M.H. Jaward, Mr P. Li, Dr Z.-Q. Lang and Dr M.-y' Chen, and
the first author's colleagues in the Faculty of Engineering at the University
of Malta.
Contents
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xv
Acronyms .................................................... xix
Mathematical Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. XXl
Part I. Introduction
1. Introduction.............................................. 3
1.1 Intelligent Control Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Approaches to Intelligent Control. . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Contribution of Adaptive Control .................. 5
1.2.2 Contribution of Artificial Intelligence ............... 6
1.2.3 Confluence of Adaptive Control and AI: Intelligent
Control. . .... .... .. . . .. . . .. .... .. ... . .. . . .. . . . . . 8
1.3 Enhancing the Performance of Intelligent Control. . . . . . . . . .. 10
1.3.1 Multiple Model Schemes: Dealing with Complexity. .. 10
1.3.2 Stochastic Adaptive Control: Dealing with Uncertainty 14
1.4 The Objectives and their Rationale. . . . . . . . . . . . . . . . . . . . . .. 16
Part II. Deterministic Systems
2. Adaptive Control of Nonlinear Systems.. . . .. ... . .... . . . .. 23
2.1 Introduction........................................... 23
2.2 Continuous-time Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23
2.2.1 Control by Feedback Linearization. . . . . . . . . . . . . . . . .. 24
2.2.2 Control by Backstepping . . . . . . . . . . . . . . . . . . . . . . . . .. 27
2.2.3 Adaptive Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29
2.3 Discrete-time Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36
2.3.1 Affine Approximations and Feedback Linearization. .. 42
2.3.2 Adaptive Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42
2.4 Summary.............................................. 46
xii Contents
3. Dynamic Structure Networks for Stable Adaptive Control 47
3.1 Introduction........................................... 47
3.2 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 49
3.3 Fixed-structure Network Solutions. . . . . . . . . . . . . . . . . . . . . . .. 50
3.4 Dynamic Network Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 54
3.5 The Control Law and Error Dynamics .................... 56
3.6 The Adaptive System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58
3.7 Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 59
3.8 Evaluation of Control Parameters and Implementation . . . . .. 62
3.8.1 The Disturbance Bound. . . . . . . . . . . . . . . . . . . . . . . . . .. 62
3.8.2 Choice of the Boundary Layer ..................... 65
3.8.3 Comments....................................... 67
3.8.4 Implementation.................................. 68
3.9 Simulation Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 70
3.9.1 Example 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 70
3.9.2 Example 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 73
3.10 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77
4. Composite Adaptive Control of Continuous-Time Systems 79
4.1 Introduction........................................... 79
4.2 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81
4.3 The Neural Networks ............ . . . . . . . . . . . . . . . . . . . . . .. 81
4.4 The Control Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83
4.5 Composite Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84
4.5.1 The Identification Model. . . . . . . . . . . . . . . . . . . . . . . . .. 84
4.5.2 The Adaptation Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 86
4.6 Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 88
4.7 Determination of the Disturbance Bounds .... . . . . . . . . . . . .. 91
4.8 Simulation Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92
4.8.1 Example 1 ..................................... " 92
4.8.2 Example 2 ................................. ; . . . .. 98
4.9 Summary .............................................. 100
5. Functional Adaptive Control of Discrete-Time Systems ... 101
5.1 Introduction ........................................... 101
5.2 Problem Formulation ................................... 102
5.3 The Neural Network .................................... 103
5.4 The Control Law ....................................... 104
5.5 The Adaptive System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 104
5.6 Stability Analysis ....................................... 105
5.7 Tracking Error Convergence ............................. 111
5.8 Simulation Examples .................................... 112
5.8.1 Example 1 ....................................... 113
5.8.2 Example 2 ..................................... " 115
5.9 Extension to Adaptive Sliding Mode Control ............... 117
Contents xiii
5.9.1 Definitions of a Discrete-time Sliding Mode .......... 117
5.9.2 Adaptive Sliding Mode Control .................... 120
5.9.3 Problem Formulation ............................. 121
5.9.4 The Control Law ................................. 122
5.9.5 The Adaptive System ............................. 122
5.9.6 Stability Analysis ................................ 123
5.9.7 Sliding and Tracking Error Convergence ............. 123
5.9.8 Simulation Example .............................. 124
5.10 Summary .............................................. 126
Part III. Stochastic Systems
6. Stochastic Control ........................................ 131
6.1 Introduction ........................................... 131
6.2 Fundamental Principles ................................. 132
6.3 Classes of Stochastic Control Problems .................... 134
6.4 Dual Control ........................................... 136
6.4.1 Degrees of Interaction ............................. 137
6.4.2 Solutions to the Implementation Problem ............ 137
6.5 Conclusions ............................................ 145
7. Dual Adaptive Control of Nonlinear Systems . . . . . . . . . . . .. 147
7.1 Introduction ........................................... 147
7.2 Problem Formulation ................................... 148
7.3 Dual Controller Design .................................. 149
7.3.1 GaRBF Dual Controller ........................... 149
7.3.2 Sigmoidal MLP Dual Controller .................... 153
7.3.3 Analysis of the Control Laws ...................... 157
7.4 Simulation Examples and Performance Evaluation .......... 158
7.4.1 Example 1 ....................................... 158
7.4.2 Example 2 ....................................... 161
7.5 Summary .............................................. 163
8. Multiple Model Approaches .............................. 165
8.1 Introduction ........................................... 165
8.2 Basic Formulation ...................................... 165
8.2.1 Multiple Model Adaptive Control. .................. 168
8.2.2 Jump Systems ................................... 170
8.3 Adaptive IO Models .................................... 178
8.3.1 Scheduled Mode Transitions ....................... 179
8.4 Summary .............................................. 185
