Artificial Neural Networks for Modelling and Control of Non-Linear Systems
Artificial neural networks possess several properties that make them particularly attractive for applications to modelling and control of complex non-linear systems. Among these properties are their universal approximation ability, their parallel network
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Artificial Neural Networks for Modelling and Control of Non-Linear Systems by
Johan A. K. Suykens Joos P. L. Vandewalle Bart L. R. De Moor
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress
ISBN 978-1-4419-5158-8 DOI 10.1007/978-1-4757-2493-6
ISBN 978-1-4757-2493-6 (eBook)
Printed on acid-free paper
All Rights Reserved
©1996 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1996 Softcover reprint ofthe hardcover 1st edition 1996
No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
Contents Preface
ix
Notation
xi
1
Introduction 1.1 Neural information processing systems 1.2 ANNs for modelling and control . 1.3 Chapter by Chapter overview 1.4 Contributions..... . . . . . .
1 1 5 8 15
2
Artificial neural networks: architectures and learning rules 2.1 Basic neural network architectures 2.2 Universal approximation theorems . . 2.2.1 Multilayer perceptrons . . . . . 2.2.2 Radial basis function networks 2.3 Classical paradigms of learning 2.3.1 Backpropagation 2.3.2 RBF networks 2.4 Conclusion
19 19 23 23 27
Nonlinear system identification using neural networks 3.1 From linear to nonlinear dynamical models 3.2 Parametrization by ANNs . . . . 3.2.1 Input/output models. . . 3.2.2 Neural state space models :3.2.3 Identifiability . . . . . . . :3.3 Learning algorithms . . . . . . . 3.:3.1 Feedforward network related models 3.:3.1.1 Backpropagation algorithm :3.3.l.2 Prediction error algorithms
37 38 39 39 41 43
3
v
28 29 33 35
45 46 46 46
Contents
vi 3.3.1.3 3.3.2
Recurrent network related models
48
"
50
3.3.2.1
Dynamic backpropagation
50
3.3.2.2
Extended KaIman filtering
54
:3.4
Elements from nonlinear optimization theory
55
3.5
Aspects of model validation, pruning and regularization
58
3.6
Neural network models as uncertain linear systems
61
:3.7
3.6.1
Convex polytope ..
62
3.6.2
LFT representation .
65
Examples . . . . . . . . . .
68
Some eh allen ging examples from the literature
68
3.7.2
Simulated nonlinear system with hysteresis
69
3.7.3
Identification of a glass furnace
75
:3.7.4
Identifying n-double scrolls
77
3.7.1
3.8
4
Extended KaIman filtering
Conclusion
82
Neural networks for cOlltrol 4.1
4.2
4.:3
83
Neural control strategies ..
8:3
4.1.1
Direct versus indirect adaptive methods
8:3
4.1.2
Reinforcement learning
85
4.1.:3
Neural optimal control .
87
4.1.4
Internal model control and model predictive control
88
Neural optimal control . . . . . . . . . . . . . . . . . . . .
90
4.2.1
The N -stage optimal control problem
4.2.2
Neural optimal contro!: full state information case
92
4.2.:3
Stabilization problem: full static state feedback Tracking problem: the LISP principle . . . .
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