Foundations of Adaptive Control

527 Pages·1991·7.13 MB·English

by  K. S. Narendra (auth.), Prof. Petar V. Kokotović (eds.)

Lecture Notes ni
Control and
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160
.V.P Kokotovic (Ed.)
Foundations of
Adaptive Control
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Series Editors
M. Thoma • A. Wyner
Advisory Board
L. D. Davisson • A. G. .J MacFarlane • H. Kwakernaak
.1, L. Massey • Ya Z. Tsypkin • A. ,J Viterbi
Editor
Prof. Petar .V Kokotovib
ECE
University of California
Santa Barbara
CA 93106
USA
ISBN 3-540-54020-2 Springer-Verlag Berlin Heidelberg NewYork
ISBN 0-387-54020-2 Springer-Verlag NewYork Berlin Heidelberg
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Acknowledgements
While many people contributed to the organization of the 1990 Grainger Lectures
and the publication of this volume, these tasks would not have been accomplished
without the tireless work of Peter Sauer and Ioannis Kanellakopoulos.
Peter $auer, Grainger Associate, was in charge of administration, finances,
publicity and social programs for the Lectures.
Ioannis Kanellakopoulos, Grainger Fellow, performed all the editorial work
for the volume, including proofreading, correcting and formatting the texts.
Financial support for the Lectures was provided by the Grainger Foundation.
Personal attention of David Grainger, President, was extremely helpful.
Petar V. Kokotovid
Grainger Professor
Preface
In the fourth decade of its development, adaptive control has reached a level at
which a critical reexamination of its foundations is useful for both theoretical and
practical purposes. A series ofs ixteen lectures, The 1990 Grainger Lectures, was
dedicated to this task. The lectures were delivered at the University of Illinois,
Urbana-Champaign, September 28-October 1, 1990. In the creative atmosphere
of intense discussions among the lecturers, the scope and content of the lectures
were expanded by the addition of new topics and most recent developments.
The result of this activity are the revised and enlarged texts in this volume. As
it becomes clear even after a cursory review of its contents, the volume has gone
far beyond its original scope of reexamining the foundations of the field. New
solutions are presented for some long-standing open problems, earlier successful
approaches are unified, new problems are formulated and some of them solved.
Indeed, the title of the volume could have been changed into "Recent Advances
in Adaptive Control". However, as all of the new results address fundamental
issues, the title Foundations of Adaptive Control is still appropriate.
The two parts of the volume deal with adaptive control of linear and nonlinear
systems, respectively. Part I contains unifications, reappraisals and new results in
adaptive linear control. Most nonlinear problem formulations in Part II are new,
and some of their solutions are likely to be further extended and generalized.
Part I opens with a view of the history of the field by one of the pioneers of
Model Reference Adaptive Control, Bob Narendra. He starts with a wise caveat
that even for a professional historian it is hard or impossible to be objective,
let alone for a deeply involved participant of many exciting events. In The
Maturing of Adaptive Control, the reader will find the wealth of information
and freshness of views that only an eyewitness report can convey.
Adaptive control has always been characterized by a great diversity of con-
cepts and algorithms and a continuous search for their unification. As such, it
has been a fertile ground for both scientists and inventors who at times speak
different languages. What both groups have been lacking is a common set of
fundamental concepts in which to communicate the properties of their inven-
tions and theories. A Conceptual Framework for Parameter Adaptive
Control by Steve Morse is a major step in this direction. In the near future, his
concept of tunability may become as common as the concept of controllability.
Just as the proofs of stability and convergence dominated the 1970s, the is-
sues of robustness were central throughout the 1980s. As the next three papers in
this volume show, the robustness issues will continue to be among the important
VI
research topics in the 1990s. Petros Ioannou, one of the leading authors on this
subject, and Aniruddha Datta have given us a self-contained detailed presenta-
tion of the state-of-the-art in Robust Adaptive Control: Design, Analysis
and Robustness Bounds. What in the 1980s appeared as a collection of un-
related modifications of adaptive algorithms is now a unified methodology for
preventing destabilizing effects of disturbances and unmodeled dynamics. The
robustness proofs are at the same time simpler and more powerful. The next two
papers present new robustness results for continuous and discrete time systems.
The main message of both Robust Contlnuous-Time Adaptive Control
by Parameter Projection by Naik, Kumar, and Ydstie, and Stability of
the Direct Self-Tuning Regulator by Ydstie, is that to achieve bounded-
ness of all the signals in the presense of disturbances and unmodeled dynamics
it is sufficient to introduce a parameter projection modification into the usual
gradient update law. Although the continuous-time result by Naik, Kumar and
Ydstie was inspired by the discrete-time result of Ydstie, their order is reversed
in order to preserve the connection with the preceding continuous-time papers.
The contribution of the Soviet Academician Tsypkiu, a pioneer of both con-
trol theory and stochastic adaptive control is at the same time historicM and
innovative. In Adaptive-Invariant Discrete Control Systems, he first re-
minds us that what today we call disturbance-rejeciion conditions appeared in
the 1940s as selec~ive-invariance conditions. This type of invariance is achievable
for disturbances generated from known models and with complete knowledge of
the plant. Tsypkin then introduces the notion of adaptive-invariant systems,
which have an anMogous invariance property when the parameters of the plant
and disturbance generator are unknown. He restricts his presentation to the so-
called interval plants, whose parameters are known to belong to given intervals.
One of the leading authors in the field of stochastic adaptive control,
P. R. Kumar, was invited to summarize the field and reexamine its foundations.
In Stochastic Adaptive System Theory: Recent Advances and a Reap-
praisal, he and Wei Ren have not only accomplished this task, but have also
completed the solution of several long-standing open problems. They first pro-
vide a unified treatment of identification, prediction and control based on the
ARMAX model and prove self-tuning and convergence properties for several
adaptive schemes. They then give new general results for parallel model adapta-
tion problems, including output-error identification and adaptive noise and echo
cancelling. It is expected that these recent results will give a new impetus to both
simpler and more fundamental developments in stochastic adaptive control.
Part II of this volume consists of five papers dealing with adaptive control of
nonlinear systems. All the authors responded to the invitation to address truly
new nonlinear problems without any linear constraints imposed on the nonlin-
earities. (Since the unknown parameters appear linearly, imposing linear growth
constraints or global Lipschitz conditions would make the problems tractable by
the methods of adaptive linear control.) The first three papers assume that the
full state vector is available for feedback. More realistic situations, where only
an output is available for measurement, are considered in the last two papers.
IIV
In Adaptive Feedback Linearizatlon of Nonlinear Systems, Koko-
tovid, Kanellakopoulos, and Morse first survey some recent results and then
design a new adaptive scheme, applicable to a much larger class osfy stems than
before. The difficulties of the global adaptive stabilization and tracking problems
are shown to increase due to two factors: level of uncertaintayn d nonlinear com-
plexity. The new systematic design procedure is applicable to the highest level of
uncertainty, but it limits the nonlinear complexity by the so-called pure-feedback
condition. Whenever this assumption is globally satisfied, the results on adaptive
stabilization and tracking are global, that is, there is no loss of globality caused
by adaptation.
A conceptually broader approach to adaptive control of nonlinear systems
is presented in Adaptive Stabilization of Nonlinear Systems by Praly,
Bastin, Pomet, and :Hang. They unify and generalize most earlier results and
classify them according to additional assumptions such as matching conditions
(i.e., uncertainty levels) and linear growth constraints. The unification is achieved
by a novel Lyapunov approach to the design of direct schemes and by general-
izations of equation error filtering and regressor filtering for indirect schemes.
The key assumption in this approach is that a Lyapunov-like function exists
and depends on the unknown parameters in a particular way. Depending on
the properties of this function, various designs are possible, including feedback
linearization designs when this function is quadratic in the transformed coor-
dinates. Possibilities of either global or only regional adaptive stabilization are
also examined.
Processes involving transfer of electromagnetic into mechanical energy re-
quire essentially nonlinear models. One of the most practical representatives of
these processes is considered in Nonlinear Adaptive Control of Induction
Motors via Extended Matching by Marino, Peresada, and VMigi. Their
adaptive design encompasses, as special cases, some earlier designs and patents.
However, the assumption of full state measurement is a practical disadvantage
which motivates the development of adaptive schemes using only output mea-
surements.
Adaptive output-feedback control of nonlinear systems is a new problem of
major theoretical and practical interest. In Global Adaptive Observers and
Output-Feedback Stabilization for a Class of Nonlinear Systems by
Marino and Tomei, this problem is addressed in two stages. First, sufficient
conditions are given for the construction of global adaptive observers for single-
output systems. The construction makes use of novel filtered transformations,
that is, nonlinear changes of coordinates driven by auxiliary filters. At the sec-
ond stage, an observer-based adaptive output-feedback control is designed for a
somewhat narrower class of systems.
A different approach to adaptive output-feedback control of nonlinear sys-
tems is presented in Adaptive Output-Feedback Control of Systems with
Output Nonlinearities by Kanellakopoulos, Kokotovic and Morse. The main
result otfh is paper is a nonlinear extension of a 1978 paper by Feuer and Morse.
Because of its complexity, this early paper is less well known than the papers
mentioned in the historical survey at the beginning oft his volume. However, in
VIII
contrast to some other results of adaptive linear control, its nonlinear general-
ization does not impose linear constraints on system nonlinearities.
This brief preview suffices to show that the papers in this volume herald a
decade of new breakthroughs in adaptive control research in the decade of the
1990s. With the already achieved unification of robust adaptive control, more
research will undoubtedly be focused on performance. A particularly challenging
task will be to develop methods to improve transients and eliminate bursting
phenomena. In stochastic adaptive control, the most recent proofs of stability
and convergence make it possible to address the robustness issue in a new way.
In nonlinear systems, adaptive control has just made its first encouraging steps.
They are likely to stimulate research leading to results applicable to larger classes
of systems. Rigorous analytical methods of adaptive control may also become a
theoretical basis for some developments in neural networks.
The intellectual depth and scientific content of adaptive control are growing
at an impressive pace. Its mature vitality is as exciting as was its youthful
impetuousness.
Petar V. Kokotovi6
Urbana, Illinois
February 1991
Contents
Part I: Adaptive Linear Control 1
The Maturing of Adaptive Control
by K. S. Narendra ............................. 3
A Conceptual Framework for Parameter Adaptive Control
by A. S. Morse ............................... 73
Robust Adaptive Control: Deslgn~ Analysis and Robustness Bounds
by P. Ioarmou and A. Datta ........................ 17
Robust Continuous-Time Adaptive Control
by Parameter Projection
by S. M. Naik, P. .~1 Kumar, and B. E. Ydstie ............. 351
Stability of the Direct Self-Tuning Regulator
by B. E. Ydstie ............................... 102
Adaptive-Invariant Discrete Control Systems
by Ya. Z. Tsypkin ............................. 932
Stochastic Adaptive System Theory: Recent Advances
and a Reappraisal
by W. Ren and P. R. Kumar ....................... 962
Part II: Adaptive Nonlinear Control 309
Adaptive Feedback Linearization of Nonlinear Systems
by P. V. Kokotovi5, I. Kanellakopoulos, and A. S. Morse ........ 113
Adaptive Stabilization of Nonlinear Systems
by L. Praly, G. Bastin, J.-B. Pomet, and Z. P. Jiang .......... 347
Adaptive Nonlinear Control of Inductlon Motors
via Extended Matching
by R. Marino, S. Peresada, and P. Valigi ................. 435
Global Adaptive Observers and Output-Feedback Stabilization
for a Class of Nonlinear Systems
by .~P Marino and P. Tomei ........................ 455
Adaptive Output-Feedback Control of Systems
with Output Nonlinearities
by I. Kanellakopoulos, P. V. Kokotovi5, and A. S. Morse ........ 495
P a r t I
A d a p t i v e Linear Control