Neural Network Systems Techniques and Applications. Volume 7. Control and Dynamic Systems

459 Pages·18.267 MB·English

by  Leondes C.T. (Ed.)

Control and
Dynamic Systems
Control and
Dynamic Systems
Neural Network Systems
Techniques and Applications
Edited by Cornelius T. Leondes
Algorithms and Architectures
VOLUME 1.
VOLUME 2. Optimization Techniques
ImplementationT echniques
VOLUME 3.
Industrial and Manufacturing Systems
VOLUME 4.
Image Processing and Pattern Recognition
VOLUME 5.
Fuzzy Logic and Expert Systems Applications
VOLUME 6.
Control and Dynamic Systems
VOLUME 7.
Control and
Dynamic Systems
Edited by
Cornelius T. Leondes
Professor Emeritus
University of California
Los Angeles, California
7
V O L U M E OF
Neural Network Systems
Techniques and Applications
ACADEMIC PRESS
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Copyright (cid:14)9 1998 by ACADEMIC PRESS
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Library of Congress Card Catalog Number: 97-80441
International Standard Book Number: 0-12-443867-9
PRINTED IN THE UNITED STATES OF AMERICA
97 98 99 00 01 02 ML 9 8 7 6 5 4 3 2 1
Contents
Contributors xiii
Preface xv
Orthogonal Functions for Systems Identification
and Control
Chaoying Zhu, Deepak Shukla, and Frank W. Paul
I. Introduction 1
II. Neural Networks with Orthogonal
Activation Functions 2
A. Background 2
B. Neural System Identification and Control 4
C. Desired Network Properties for System Identification
and Control 5
D~ Orthogonal Neural Network Architecture 7
E. Gradient Descent Learning Algorithm 12
F. Properties of Orthogonal Activation Function-Based
Neural Networks 14
G~ Preliminary Performance Evaluation of Orthogonal
Activation Function-Based Neural Networks 21
III. Frequency Domain Applications Using Fourier Series
Neural Networks 25
A. Neural Network Spectrum Analyzer 25
B. Describing Function Identification 33
C. Fourier Series Neural Network-Based Adaptive
Control Systems 35
vi Contents
IV. Time Domain Applications for System Identification
and Control 47
A. Neural Network Nonlinear Identifier 47
B. Inverse Model Controller 55
C. Direct Adaptive Controllers 58
V. Summary 71
References 72
Multilayer Recurrent Neural Networks for
Synthesizing and Tuning Linear Control Systems via
Pole Assignment
Jun Wang
I. Introduction 76
II. Background Information 77
III. Problem Formulation 79
IV. Neural Networks for Controller Synthesis 85
V. Neural Networks for Observer Synthesis 93
VI. Illustrative Examples 98
VII. Concluding Remarks 123
References 125
Direct and Indirect Techniques to Control Unknown
Nonlinear Dynamical Systems Using Dynamical
Neural Networks
George A. Rovithakis and Manolis A. Christodoulou
I. Introduction 127
A. Notation 129
II. Problem Statement and the Dynamic Neural
Network Model 130
III. Indirect Control 132
A. Identification 132
B. Control 134
IV. Direct Control 139
A. Modeling Error Effects 140
B. Model Order Problems 148
Contents vii
V. Conclusions 154
References 154
A Receding Horizon Optimal Tracking Neurocontroller
for Nonlinear Dynamic Systems
Young-Moon Park, Myeon-Song Choi, and Kwang Y. Lee
I. Introduction 158
II. Receding Horizon Optimal Tracking Control
Problem Formulation 159
A. Receding Horizon Optimal Tracking Control Problem
of a Nonlinear System 159
B. Architecture for an Optimal
Tracking Neurocontroller 162
III. Design of Neurocontrollers 163
A. Structure of Multilayer Feedforward
Neural Networks 163
B. Identification Neural Network 164
C. Feedforward Neurocontroller 168
D. Feedback Neurocontroller 170
E. Generalized Backpropagation-through-
Time Algorithm 171
IV. Case Studies 176
A. Inverted Pendulum Control 176
B. Power System Control 180
V. Conclusions 187
References 188
On-Line Approximators for Nonlinear System
Identification: A Unified Approach
Marios M. Polycarpou
I. Introduction 191
II. Network Approximators 193
A. Universal Approximators 194
B. Universal Approximation of Dynamical Systems 197
C. Problem Formulation 199
viii Contents
III. Learning Algorithm 200
A. Weight Adaptation 202
B. Linearly Parametrized Approximators 206
C. Multivariable Systems 208
IV@ Continuous-Time Identification 210
A. Radial-Basis-Function Network Models 213
B. Multilayer Network Models 223
Vo Conclusions 228
References 229
The Determination of Multivariable Nonlinear Models
for Dynamic Systems
S. A. Billings and S. Chen
I. Introduction 231
II. The Nonlinear System Representation 233
III. The Conventional NARMAX Methodology 235
A. Structure Determination and
Parameter Estimation 236
B. Model Validation 245
IV@ Neural Network Models 246
A. Multilayer Perceptrons 247
B. Radial Basis Function Networks 248
C. Fuzzy Basis Function Networks 251
D. Recurrent Neural Networks 252
VO Nonlinear-in-the-Parameters Approach 254
A. Parallel Prediction Error Algorithm 255
B. Pruning Oversized Network Models 257
VI@ Linear-in-the-Parameters Approach 259
A. Regularized Orthogonal Least-Squares Learning 262
B. Enhanced Clustering and
Least-Squares Learning 267
C. Adaptive On-Line Learning 271
VII. Identifiability and Local Model Fitting 271
VIII. Conclusions 273
References 275
Contents ix
High-Order Neural Network Systems in the
Identification of Dynamical Systems
Elias B. Kosmatopoulos and Manolis A. Christodoulou
I. Introduction 279
II. RHONNs and g-RHONNs 281
III. Approximation and Stability Properties of RHONNs
and g-RHONNs 284
A. Stability and Robustness Properties
of g-RHONNs 286
IV. Convergent Learning Laws 289
A. Robust Adaptive Learning Laws 290
B. Learning Laws That Guarantee Exponential
Error Convergence 292
V. The Boltzmann g-RHONN 294
VI. Other Applications 298
A. Estimation of Robot Contact Surfaces 298
B. RHONNs for Spatiotemporal Pattern Recognition and
Identification of Stochastic Dynamical Systems 300
C. Universal Stabilization Using High-Order
Neural Networks 301
VII. Conclusions 304
References 304
Neurocontrols for Systems with Unknown Dynamics
William A. Porter, Wie Liu, and Luis Trevino
I. Introduction 307
II. The Test Cases 309
III. The Design Procedure 313
A. Using Higher Order Moments 314
B. Embedding the Controller Design in H(v) 315
C. HOMNA Training Algorithms 316
D. Tensor Space Matchups with the
HOMNA Calculations 318
IV. More Details on the Controller Design 318