Table Of ContentAdvanced Textbooks in Control and Signal Processing
Springer-Verlag London Ltd.
Series Editors
Professor Michael J. Grimble, Professor of Industrial Systems and Director
Professor Michael A. Johnson, Professor of Control Systems and Deputy Director
Industrial Control Centre, Department of Electronic and Electrical Engineering,
University of Strathc1yde, Graham Hills Building, 50 George Street, Glasgow GllQE, U.K.
Other titles published in this series:
Genetic Algorithms
K.F. Man, K.S. Tang and S. Kwong
Model Predictive Control
E.F. Camacho and C. Bordons
Introduction to Optimal Estimation
E.W. Kamen and J. Su
Discrete-time Signal Processing
D. Williamson
Neural Networks for Modelling and Control of Dynamic Systems
M. N0rgaard, O. Ravn, L.K. Hansen and N.K. Poulsen
Modelling and Control of Robot Manipulators (2nd Edition)
L. Sciavicco and B. Siciliano
Fault Detection and Diagnosis in Industrial Systems
L.H. Chiang, E.L. Russell and R.D. Braatz
Statistical Signal Processing
T. Chonavel and S. Vaton
Publication Due April 2001
L. Fortuna, G. Rizzotto, M. Lavorgna,
G. Nunnari, M.G. Xibilia and R. Caponetto
Soft Computing
New Trends and Applications
With 193 Figures
Springer
Professor Luigi Fortuna
Dipartimento Elettrico Elettronico e Sistemistico, Universita di Catania, Viale A.
Doria 6,95125 Catania, Italy
Doctor Gianguido Rizzotto
Doctor Mario Lavorgna
STMicroelectronics, Stradale Primosole 50,95121 Catania, Italy
Professor Giuseppe Nunnari
Professor M. Gabriella Xibilia
Doctor Riccardo Caponetto
Dipartimento Elettrico Elettronico e Sistemistico, Universita di Catania, Viale A.
Doria 6, 95125 Catania, Italy
ISSN 1439-2232
ISBN 978-1-85233-308-9
British Library Cataloguing in Publication Data
Soft Computing: new trends and applications. -(Advanced
Textbooks in control and signal processing)
l.$oft computing
LFortuna, L.
006.3
ISBN 978-1-85233-308-9
Library of Congress Cataloging-in-Publication Data
Soft computing: new trends and applications 1 L. Fortuna ... let al.].
p. cm. - (Advanced textbooks in control and signal processing)
Includes bibliographical references.
ISBN 978-1-85233-308-9 ISBN 978-1-4471-0357-8 (eBook)
DOI 10.1007/978-1-4471-0357-8
1. Soft computing. L Fortuna, L. (Luigi), 1953-II. Series.
QA76.9.S63 56334 2000
006.3-dc21 00-046342
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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be sent to the publishers.
© Springer-Verlag London 2001
Originally published by Springer-Verlag London Limited in 2001
Additional material to this book can be downloaded from http//extras.springer.com.
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The publisher makes no representation, express or implied, with regard to the accuracy of the
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Typesetting: Electronic text files prepared by authors
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Series Editors' Foreword
The topics of control engineering and signal processing continue to flourish and
develop. In common with general scientific investigation, new ideas, concepts and
interpretations emerge quite spontaneously and these are then discussed, used,
discarded or subsumed into the prevailing subject paradigm. Sometimes these
innovative concepts coalesce into a new sub-discipline within the broad subject
tapestry of control and signal processing. This preliminary battle between old and
new usually takes place at conferences, through the Internet and in the journals of
the discipline. After a little more maturity has been acquired has been acquired by
the new concepts then archival publication as a scientific or engineering
monograph may occur.
A new concept in control and signal processing is known to have arrived when
sufficient material has developed for the topic to be taught as a specialised tutorial
workshop or as a course to undergraduates, graduates or industrial engineers. The
Advanced Textbooks in Control and Signal Processing series is designed as a
vehicle for the systematic presentation of course material for both popular and
innovative topics in the discipline. It is hoped that prospective authors will
welcome the opportunity to publish a structured presentation of either existing
subject areas or some of the newer emerging control and signal processing
technologies.
Fuzzy logic, neural networks and genetic algorithms have excited much interest
among control engineering practitioners. This interest has arisen because these
methods are able to solve a new set of control engineering and signal processing
problems, which are more loosely defined and sometimes involve a degree of
operational uncertainty. Fortuna et al. tackle the problems of image processing,
greenhouse temperature control, urban traffic noise monitoring, a robot for picking
citrus fruit, a rapid thermal processing oven and air pollution control in this new
course textbook for the Advanced Textbooks in Control and Signal Processing
series. This is a very interesting set of real applications problems and for the first
time in the textbook series the emerging technologies have been treated as a
solution paradigm for these problems. Thus the book first creates the pedagogical
basis for the subject in early chapters on fuzzy logic, fuzzy control, artificial neural
networks and so on, before progressing to the descriptions and solutions of the
applications problems.
This textbook presentation of the emerging technologies should be invaluable
for new courses in this area, since all the approaches are presented together. The
Vi Series Editors' Foreword
textbook should also be useful for advanced undergraduate projects, and home
study by practising engineers.
MJ. Grimble and M.A. Johnson
Industrial Control Centre
Glasgow, Scotland, U.K.
October, 2000
Preface
Since the invention of the transistor in the 1947, the semiconductor industry has
passed from manufacture of a single component to that of a device, containing
more than a billion transistors, integrated in a few square centimeters of silicon.
In the last 25 years, there has been an annual reduction of 26 per cent in the
price of a bit; nowadays, memory of more than a billion bits and teraflops (1012
floating point operations per second) processors are produced. This technological
development cannot be compared with those in other industrial activities.
If the automotive industry had proceeded with the same speed, a car could cost
about ten dollars, its top speed would be very close to light speed and with just a
little bit more than a liter of fuel, it could be possible to cover ten times distance
from the Earth to the Moon; so it is easy to guess how microelectronics has had
such an important role in the process of welfare and the improvement of the quality
of life and it is easy to believe that this will be the tendency in years to come. After
this preliminary statement, soft computing's computational theory seems to be able
to accept the challenge.
Soft computing's purpose is to keep up the techno-scientific project, started in
the eighties with fuzzy logic, first in Japan and then in the West, where the
complexity, the non-linearity, the uncertainty, intrinsic properties of real processes
and phenomena, are no longer considered as a limit for the planning of the systems
but on the contrary, as the starting-point for the study of new inferential
mechanisms and non-conventional algorithms for the creation of more tolerant,
robust and cheaper products.
In other words, soft computing is an antithesis of hard computing: it provides
algorithms that are able to value, to reason and to discriminate, rather than just to
'calculate'; these new structures of calculation are based on logic with more values
(not just true or false, but different degrees of certainty) and inspired by natural
processes like selection, aggregation and co-operation.
At full speed, soft computing, together with the technology of integration,
makes it possible, from today, to plan more intelligent and easier-to-use machines,
increasing the quality of our daily life, in both social and work environments.
Thanks to scientific collaboration with a lot of universities, STMicroelectronics
can be proud of a center of excellence for planning intelligent products, based on
soft computing methodologies, that are involved in automotive and electronic
systems, servo-systems for industrial applications, consumer products, and so on.
This book arises from the co-operation between the academic world, and in
particular between the University of Catania and STMicroelectronics.
viii Preface
The authors synthesize the most important results of this decennial
collaboration in a clear and complete way.
The bilateral industry-university results, are, once again, not just successful, but
also, the only way to transfer innovative ideas from the research world to the
industrial one, in a short time, making, the gift of soft computing methodologies at
the disposal of society.
Salvatore Castorina
STMicroelectronics Corporate Vice-President
Table of Contents
1. Introduction ....................................................................................................... 1
2. Fuzzy Logic ........................................................................................................ 5
2.1 Introduction ................................................................................................ 5
2.2 Fuzzy Sets .................................................................................................. 6
2.3 Fuzzy Set Operations ................................................................................. 8
2.4 Fuzzy Algorithms .................................................................................... 10
2.5 The Fuzzy Algorithm with a Linear Consequent.. ................................... 16
2.6 Determining the Fuzzy Algorithm ........................................................... 17
2.7 An Example: Controlling the Inverse Pendulum ..................................... 18
2.8 References ................................................................................................ 20
3. Fuzzy Control .................................................................................................. 23
3.1 Introduction .............................................................................................. 23
3.2 A Systematic Approach for the Design of a Fuzzy Control System ........ 24
3.3 Synthesis and Validation of a Fuzzy Controller ...................................... 26
3.3.1 Determining the Control Laws .................................................... 27
3.3.2 Determining the Fuzzy Controller ............................................... 29
3.3.3 Validating the Fuzzy Controller .................................................. 30
3.4 An Example: The Control ofa Switching Converter ............................... 35
3.5 References ................................................................................................ 51
4. Artificial Neural Networks ............................................................................. 53
4.1 Introduction. ............................................................................................. 53
4.2 The Multilayer Perceptron ....................................................................... 56
4.3 Non-supervised Neural Networks ............................................................ 63
4.4 Radial Basis Function Neural Networks .................................................. 66
4.5 Applications ............................................................................................. 72
4.5.1 Example: Interpolation of a Non-linear Map ............................... 72
4.5.2 Example ofRBF as a Classifier: Diagnostic Aboard a Rail
Road ............................................................................................. 75
4.6 References ................................................................................................ 77
5. Neural Networks for Modeling and Controlling Dynamical Systems ....... 81
5.1 Identification of Non-linear Systems ....................................................... 81
5.2 Identification by Means of Neural Networks ........................................... 83
x Table of Contents
5.3 Effects of Disturbance and Uncertainty ................................................... 85
5.4 Example ofIdentification by Means ofa Neural Network.. .................... 87
5.5 Neural Control ......................................................................................... 90
5.6 Feed-forward Control with Identification of the Inverse Dynamics ........ 91
5.7 The CMAC Control Scheme .................................................................... 93
5.8 References ................................................................................................ 96
6. Evolutionary Optimization Algorithm .......................................................... 97
6.1 Introduction .............................................................................................. 97
6.2 The Structure of a Genetic Algorithm ...................................................... 99
6.3 A Numerical Example ........................................................................... 104
6.4 The Schema Theorem ............................................................................ 108
6.5 How to Improve the Performance ofa Genetic Algorithm .................... 110
6.6 References .............................................................................................. 115
7. Cellular Neural Networks ............................................................................ 117
7.1 Introduction ................................................................................................. .
7.2 The Architecture of Cellular Neural Networks: The Electrical Model.. 117
7.3 Stability ofa Cellular Neural Network .................................................. 122
7.4 Behavior ofa Cellular Neural Network Circuit ..................................... 125
7.5 Applications of Cellular Neural Networks to Image Processing ........... 126
7.5.1 Static Image Applications .......................................................... 127
7.5.2 Automatic Generation of Templates .......................................... 129
7.5.3 Enlargement and Reconstruction ofImages .............................. 131
7.6 References .............................................................................................. 133
8. Complex Dynamics and Cellular Neural Networks ................................... 135
8.1 Introduction ............................................................................................ 135
8.2 Notes on Dynamical Systems ................................................................ 135
8.3 Chaotic Systems ..................................................................................... 144
8.4 The Lyapunov Exponents ...................................................................... 149
8.5 Dimension of the Attractors ................................................................... 152
8.6 Circuit Models of Chaotic Dynamic Systems ........................................ 154
8.6.1 The Duffing Oscillator .............................................................. 155
8.6.2 Chua's Circuit ............................................................................ 155
8.6.3 The Lorenz Circuit .................................................................... 157
8.7 Generating Chaotic Phenomena by CNN .............................................. 158
8.7.1 Implementing a Chua Circuit by Means ofCNN ...................... 159
8.7.2 SC-CNNs as a Platform for Generating Other Chaotic
Dynamics ................................................................................... 162
8.8 References .............................................................................................. 167
9. Neuro-fuzzy Networks .................................................................................. 169
9.1 Introduction. ........................................................................................... 169
9.2 Neuro-fuzzy Network Architecture ....................................................... 170
9.3 Learning Algorithms For Neuro-fuzzy Networks .................................. 173
9.4 Example: Interpolating a Non-linear Map with a Fuzzy Model ............ 174
