Essays on Control: Perspectives in the Theory and its Applications

439 Pages·1993·12.135 MB·English

by  A. G. J. MacFarlane (auth.), H. L. Trentelman, J. C. Willems (eds.)

Progress in Systems and Control Theory
Volume 14
Series Editor
Christopher I. Byrnes, Washington University
Associate Editors
S.-I. Amari, University of Tokyo
B.D.O. Anderson, Australian National University, Canberra
Karl Johan AstrlSm, Lund Institute of Technology, Sweden
Jean-Pierre Aubin, EDOMADE, Paris
H.T. Banks, North Carolina State University, Raleigh
John S. Baras, University of Maryland, College Park
A. Bensoussan, INRIA, Paris
John Burns, Virginia Polytechnic Institute, Blacksburg
Han-Fu Chen, Academia Sinica, Beijing
M.H.A. Davis, Imperial College of Science and Technology, London
Wendell Fleming, Brown University, Providence, Rhode Island
Michel Fliess, CNRS-ESE, Gif-sur-Yvette, France
Keith Glover, University of Cambridge, England
Diederich Hinrichsen, University of Bremen, Germany
Alberto Isidori, University of Rome
B. Jakubczyk, Polish Academy of Sciences, Warsaw
Hidenori Kimura, University of Osaka
Arthur J. Krener, University of California, Davis
H. Kunita, Kyushu University, Japan
Alexander Kurzhansky, Academy of Sciences, Russia
Harold J. Kushner, Brown University, Providence, Rhode Island
Anders Lindquist, Royal Institute of Technology, Sweden
Andrzej Manitius, George Mason University, Fairfax, Virginia
Clyde F. Martin, Texas Tech University, Lubbock, Texas
Sanjoy Mitter, Massachusetts Institute of Technology, Cambridge
Giorgio Picci, University of Padova, Italy
Boris Pshenichnyj, Glushkov Institute of Cybernetics, Kiev
H. J. Sussmann, Rutgers University, New Brunswick, New Jersey
T. J. Tarn, Washington University, St. Louis, Missouri
V. M. Tikhomirov, Institute for Problems in Mechanics, Moscow
Pravin P. Varaiya, University of California, Berkeley
Jan C. Willems, University of Groningen, The Netherlands
W. M. Wonham, University of Toronto
Essays on Control:
Perspectives in the Theory
and its Applications
H. L. Trentelman
c.
J. Willems
Editors
Springer Science+Business Media, LLC
H. L. Trentelman J. C. Willems
University of Groningen University of Groningen
Mathematics Institute Mathematics Institute
The Netherlands The Netherlands
Library of Congress Cataloging In-Publication Data
Essays on control : perspectives in the theory and its applications /
H. L. Trentelman, J. C. Willems, editors.
p. cm. -- (Progress in systems and control theory : v. 14)
Inc1udes bibliographical references.
ISBN 978-1-4612-6702-7 ISBN 978-1-4612-0313-1 (eBooK)
DOI 10.1007/978-1-4612-0313-1
1. Control theory. I. Trentelman, H. L. 11. Willems, Jan C.
III. Series.
QM02.3.E87 1993 93-1980
003'.5--dc20 CIP
Printed on acid-free paper
© Springer Science+Business Media New York 1993
Originally published by Birkhäuser Boston in 1993
Softcover reprint ofthe hardcover 2nd edition 1993
Second printing 1994
Copyright is not claimed for works ofU.S. Government employees.
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ISBN 978-1-4612-6702-7
Typeset by the Authors in TEX.
987 654 3 2
Contents
Information, Knowledge and Control
A. G.J. MacFarlane . . . . . . 1
Hybrid Models for Motion Control Systems
R. W. Brockett ........... ..•.....• 29
Some Control Problems in the Process Industries
M. Morari . . . . . . . . . . . . .. ......•.. 55
Engineering Aspects of Industrial Applications
of Model-Based Control Techniques and System Theory
A.C.P.M. Backz .............. ...••• 79
Towards a Joint Design of Identification and Control?
M. Gevers ............ . 111
Nonlinear State Space 'Hoo Control Theory
A. J. van der Schaft . . . . . . . 153
Learning Control and Related Problems
in Infinite-Dimensional Systems
Y. Yamamoto ..... . 191
An Algebraic Approach to Linear and Nonlinear Control
M. Fliess, S. T. Glad .......... . 223
Robust Multivariable Control Using 'Hoo Methods:
Analysis, Design and Industrial Applications
1. Postlethwaite, S. Skogestad .... 269
Neural Networks for Control
E.D. Sontag . . . . . 339
Neural Networks for Adaptive Control and Recursive
Identification: A Theoretical Framework
J.-J.E. Slotine and R.M. Sanner 381
Preface
This book contains the text of the plenary lectures and the mini-courses
of the European Control Conference (ECC'93) held in Groningen, the
Netherlands, June 2S-July 1, 1993. However, the book is not your usu
al conference proceedings. Instead, the authors took this occasion to take
a broad overview of the field of control and discuss its development both
from a theoretical as well as from an engineering perpective.
The first essay is by the key-note speaker ofthe conference, A.G.J. Mac
Farlane. It consists of a non-technical discussion of information processing
and knowledge acquisition as the key features of control engineering tech
nology.
The next six articles are accounts of the plenary addresses.
The contribution by R.W. Brockett concerns a mathematical framework
for modelling motion control, a central question in robotics and vision.
In the paper by M. Morari the engineering and the economic relevance
of chemical process control are considered, in particular statistical quality
control and the control of systems with constraints.
The article by A.C.P.M. Backx is written from an industrial perspec
tive. The author is director of an engineering consulting firm involved in
the design of industrial control equipment. Specifically, the possibility of
obtaining high performance and reliable controllers by modelling, identifi
cation, and optimizing industrial processes is discussed.
One of the most active areas of control theory research goes under the
somewhat cryptic name of H oo-control. The fundamental problem is to
obtain feedback control algorithms such that the performance, measured
in terms of the induced L2-norm from the disturbance input to the to-be
controlled output, is minimized. The paper by A.J. van der Schaft gives an
overview of the Hoo-problem for nonlinear systems.
In the article by M. Gevers an overview of an emerging area of con
trol theory research is presented: the problem of obtaining identification
algorithms for use in the design of robust controllers.
Distributed parameter systems form the topic of Y. Yamamoto's essay,
in which the issue of learning control is addressed.
In addition to these plenary lectures and several hundreds of contributed
papers, there were three mini-courses given at the ECC'93. These three-
Vlll Preface
hour courses were based on tutorial expose's of recent developments in
control, illustrating advances in both theoretical as well as the engineer
ing aspects of the field. The first mini-course was based on the article by
M. Fliess and S.T. Glad, explainiLg the use of differential algebra as a math
ematical framework for describing systems by means of models involving
differential equations.
The second mini-course was based on the article by I. Postlethwaite
and S. Skogestad, in which the methodology in designing robust industrial
controllers using Hoo-methods is explained.
The third mini-course at the ECC'93 was devoted to the emerging field
of neural networks. It was based on the article by E.D. Sontag on neural
networks in control, and the article by J .-J. Slotine and R.M. Sanner on
neural networks for adaptive control and identification.
We would like to take this occasion to thank all those who have con
tributed to this book. A special word of thanks goes to our colleague Rein
Smedinga who has lend us his DTEJX expertise for formatting this book.
Groningen, April 6, 1993
The editors:
Harry 1. Trentelman
Jan C. Willems.
1. Information, Knowledge and
Control
A.G.J. MacFarlane*
Abstract
The importance of control has led to the development of one of
the modern world's key technologies, and one whose use will increase
rather than diminish. As such it needs a coherent philosophy - a
world view, a conceptual framework which will allow the fundamen
tal problems which confront its developers to be posed, which will
allow its nature to be explained to non- specialists in an illuminating
way, which will ensure that its fundamental concerns are not over
looked in an ever-increasing welter of specialisation and diversity of
application, and which will ensure that it maintains a proper balance
between theory and practice.
The basic concepts of : data and process, information, complex
ity and interaction are used to indicate the potential importance of
information- theoretic concepts for such an undertaking. Much of
the exposition draws on Kolmogorov's measure of algorithmic com
plexity, and analogies are drawn between the properties of effective
interaction and the fundamental Laws of Thermodynamics.
Control is regarded as a technology which must necessarily draw
on a range of cognate fields. Any resolutions of the fundamental
problems which it faces in further developing as a technology will,
it is claimed, share certain key features : they will use information
theoretic concepts; they will harness an emerging technology of knowl
edgeable machines to help manage the complexity of the data gen
erated by theory; they will draw widely on, and interact with, a
widening range of cognate fields; and they increasingly will adopt a
pragmatic and empirical approach.
1 Introduction
Control is effective interaction: a bird hovering and an aircraft landing are
both examples of objects interacting with their environments in a controlled
"Lord Balerno Building, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS,
Scotland, UK
2 1. Information, Knowledge and Control
way. That one of these examples is biological and one is technological shows
why the idea of control is so important: it is a concept of the widest ranging
applicability. The importance of control has led to the development of one
of the modern world's key technologies, and one whose use will increase
rather than diminish. As such it needs a coherent philosophy - a world
view, a conceptual framework which will allow the fundamental problems
which confront its developers to be posed, which will allow its nature to be
explained to non-specialists in an illuminating way, which will ensure that
its fundamental concerns are not overlooked in an ever-increasing welter
of specialisation and diversity of application, and which will ensure that it
maintains a proper balance between theory and practice.
It is the purpose of this overview to address this difficult task; not in
any sense by offering a fully worked out philosophy of control - that would
be a huge and complex undertaking, involving many points of view and so
requiring the concerted efforts of many people - but rather by considering
a few key aspects. Subsidiary aims are to identify a number of key sources
in cognate fields which can provide access points for further study of major
relevant topics and concepts, and to consider future development.
Major, coherent domains of knowledge are characterised by a funda
mental, extensively used and essentially unifying concept : for example the
cell in biology. Control is such a coherent domain, and its fundamental uni
fying concept is that of feedback. This concept is so widely useful that it has
generated one of the few terms associated with modern technology which
have passed into the currency of everyday speech. A synoptic overview
of feedback and its many uses has been given by MacFarlane (1976), [16].
Feedback is the principal weapon in the armoury of the control system
designer. At the most basic level of description however, the terms interac
tion, feedback and control are equivalent and may be used interchangeably.
Consider for example a simple interconnection of a spring and a mass. Such
a dynamical system can be represented, in a block diagram showing the in
terrelationship of the key dynamical variables, as a feedback system. We
can, and indeed often do, speak of the spring as controlling the position
of the mass. Thus we may, usefully and as appropriate, regard the same
system in terms of a pair of interacting objects, in feedback terms, or in
terms of control.
Control is delimited as a subject by:
• its focus on a clear and simply stated problem - the achievement of
effective interaction
• by the fact that this problem generates clean interfaces with cognate
fields
• by the rich resonances which its basic concern of the achievement of
effective interaction sets up with mathematics, dynamics, informa-
A.G.J. MacFarlane 3
tion theory, physiology, neurophysiology, computational science and
artificial intelligence.
An acid test of any claim for the coherency and wide utility of a subject
is that its central purposes, and the fundamental nature of its limitations,
should be communicable to a lay audience in terms of a few fundamental
ideas. What is being attempted here is such a synoptic overview in terms
of: data and process, information, complexity and interaction.
2 Data and process
H.A. Simon, in his analysis of artefacts and systems and their uses, distin
guishes between two fundamentally different types of description :
• state descriptions, and
• process descriptions.
In his words (Simon (1981), [28]):
These two modes of apprehending structures are the warp
and weft of our experience. Pictures, blueprints, most dia
grams, and chemical structural formulas are state descriptions.
Recipes, differential equations, and equations for chemical re
actions are process descriptions. The former characterise the
world as sensed; they provide the criteria for identifying ob
jects, often by modelling the objects themselves. The latter
characterise the world as acted upon; they provide the means
for producing or generating objects having the desired charac
teristics.
Since the term state is used in dynamics and control in a very well estab
lished but very different sense, we will use the terms data description and
process description to make Simon's distinction. For example in a computer
we can store a picture of a circle as a bit map - a data description - and
print from that, or as a program to generate points lying on the circle - a
process description - and output the same picture in a different way, with
the same end result. However the amounts of information involved in the
two cases will not be the same; in general the amount of information re
quired for the process description can be much less than that for the data
description. Indeed, as we store data for more and more points, the infor
mation required for the data description can become unbounded while the
information required for the process description remains small.
Any computation carried out by an information processor will involve
a mixture of data and p~ocess. Explanatory processes underpin all our