Progress in Systems and Control Theory - rd.springer.com978-1-4757-2105-8/1.pdf · John Bums,...
Transcript of Progress in Systems and Control Theory - rd.springer.com978-1-4757-2105-8/1.pdf · John Bums,...
Progress in Systems and Control Theory Volume2
Series Editor
Christopher I. Byrnes, Washington University
Associate Editors
S.-1. Amari, University of Tokyo, Japan B.D.O. Anderson, Australian National University, Canberra, Australia Karl J. Äström, Lund Institute of Technology, Lund, Sweden Jean-Pierre Aubin, CEREMADE, Paris, France H.T. Banks, University of Southem Califomia, Los Angeles, Califomia John S. Baras, University of Maryland, College Park, Maryland A. Bensoussan, INRIA, Paris, France John Bums, Virginia Polytechnic Institute, Blacksburg, Virginia Han-Fu Chen, Beijing University, People's Republic of China M.H.A. Davis, Imperial College of Science and Technology, London,
England WendelI Fleming, Brown University, Providence, Rhode Island Michel Fliess, CNRS-ESE, Gif-sur-Yvette, France Keith Glover, University of Cambridge, Cambridge, England D. Hinrichsen, University of Bremen, Federal Republic of Germany Alberto Isidori, University of Rome, Italy B. Jakubczyk, AcademyofSciences, Warsaw, Poland Hidenori Kimura, Osaka University, Japan Arthur Krener, University of Califomia, Davis H. Kunita, Kyushu University, Japan Alexandre Kurzhansky, IIASA, Laxenburg, Austria Harold M. Kushner, Brown University, Providence, Rhode Island Anders Lindquist, Royal Institute of Technology, Stockholm, Sweden Andrzej Manitius, George Mason University, Fairfax, Virginia Clyde F. Martin, Texas Tech University, Lubbock, Texas Sanjoy Mitter, Massachusetts Institute of Technology, Cambridge,
Massachusetts Giorgio Picci, LADSEB-CNR, Padova, Italy Hector Sussman, Rutgers University, New Brunswick, New Jersey T.J. Tarn, Washington University, St. Louis, Missouri Pravin P. Varaiya, University of Califomia, Berkeley Jan C. Willems, University of Gröningen, Sweden W.M. Wonham, University of Toronto, Canada
B. Jakubczyk K. Malanowski W. Respondek
Perspectives in Control Theory
Proceedings of the Sielpia Conference, Sielpia, Poland, September 19-24, 1988
With 10 Illustrations
1990 Springer Science+Business Media, LLC
B. Jakubczyk Institute of Mathematics Polish Academy of Sciences 00-950 Warsaw Poland
W. Respondek Institute of Mathematics Polish Academy of Sciences 00-950 Warsaw Poland
K. Malanowski Systems Research Institute Polish Academy of Sciences 01-447 Warsaw Poland
Library of Congress Cataloging-in-Publication Data Perspectives in control theory: proceedings of the Sielpia Conference,
Sielpia, Poland, 1988/ B. Jakubczyk, K. Malanowski, W. Respondek.
p. cm.-(Progress in systems and control theory: v. 2) Includes bibliographical references.
1. Control theory-Congresses. I. Jakubczyk, Bronislaw. 11. Malanowski, Kazimierz. III. Respondek, W. IV. Series. QA402.3.P39 1990 629.8'312-dc20 89-18337
Printed on acid-free paper.
ISBN 978-1-4757-2107-2 ISBN 978-1-4757-2105-8 (eBook) DOI 10.1007/978-1-4757-2105-8
© Springer Science+Business Media New York, 1990 Originally published by Birkhäuser Boston in 1990. Softcover reprint ofthe hardcover 1st edition 1990
All rights reserved. No part ofthis publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permission ofthe copyright owner. Permission to photocopy for internal or personal use, or the internal or personal use of specific clients, is granted by Birkhäuser Boston, Inc., for libraries and other users registered with the Copyright Clearance Center (CCCl, provided that the base fee of $0.00 per copy, plus $0.20 per page is paid directly to CCC, 21 Congress Street, Salem, Springer Science+Business Media, LLC.
Camera-ready text provided by the individual authors.
9 8 7 6 543 2 1
Preface The volume contains papers based on lectures delivered during the school "Per
spectives in Control Theory" held in Sielpia, Poland on September 19-24, 1988. The aim of the school was to give the state-of-the-art presentation of recent
achievements as weH as perspectives in such fields of control theory as optimal control and optimization, linear systems, and nonlinear systems. Accordingly, the volume includes survey papers together with presentations of some recent results.
The special emphasis is put on:
- nonlinear systems (algebraic and geometric methods),
- optimal control and optimization (general problems, distributed parameter
systems),
- linear systems (linear-quadratic problem, robust stabilization). An important feature of the school (and consequently of the volume) was its
really "international" character since it brought together leading control theoriests
from West and East. All together the school was attended by 108 participants
from 18 countries. During the school 21 one-hour invited lectures were delivered.
Moreover, five half-an-hour talks were given and 30 contributions were presented
in frames of poster sessions.
The school was organized and supported by: Institute of Mathematics of the Polish Academy of Sciences,
Committee of Automatic Control and Robotics of the Polish Academy
of Sciences, - Institute of Automatic Control, Warsaw University of Technology (as Co
ordinator of the Basic Research Program R.P.I.02 "Theory of Control of Continuous Dynamic Systems and Discrete Processes" ).
The organizing committe consisted of: B. Frelek, B. Jakubczyk, T. Kaczorek,
M. Koci!(cki, K. Malanowski (vice-chairman), M. Niezg6dka, A. Olbrot, C. Olech
(chairman), W. Respondek (secretary), A. Sosnowski, A. Wierzbicki.
We would like to thank Ms. M. Wolinska for her excelent typing of some of the
manuscripts.
Warsaw, August 1989.
B. JAKUBCZYK
K. MALANOWSKI
w. RESPONDEK
Contents
Preface .............................................................................................. v List of Invited Speakers .................................................................. x Addresses of Contributors ............................................................... xi
1. Remarks on the Stabilizability of Nonlinear Systems by Smooth Feedback ................................................................. 1 DIRKAEYELS
2. Some Remarks on Pontryagin's Maximum Principle for Infinite Dimensional Control Problems ............................. 12 H.O. FA'ITORINI
3. State-Variable Representation Revisited, Application to Some Control Problems ....................................................... 26 MICHEL FLIESS
4. Linear-Quadratic Problems and the Riccati Equation ..... 39 A.H.W. GEERTS and M.L.J. HAUTUS
5. Robustness Measures for Linear State-Space Systems Under Complex and Real Parameter Perturbations ......... 56 D. HINRICHSEN and A.J. PRITCHARD
6. Singular Optimal Problems ................................................ 75 V. JURDJEVIC
7. Stochastic Realization of Stationary Processes: State-Space, Matrix Fraction, and ARMA Forms ....................... 89 L. KEVICZKY and J. BOKOR
8. Contributions to Nonlinear Inverse Problems Arising in Parameter Estimation for Elliptic Systems ....................... 108 K. KUNISCH
Vlll
9. Fuller's Phenomena ............................................................. 129 I.A.K KUPKA
10. Funnel Equations and Multivalued Integration Problems for Control Synthesis ........................................................... 143 A.B. KURZHANSKI and 0.1. NIKONOV
11. Output Tracking Through Singularities ............................ 154 F. LAMNABHI-LAGARRIGUE, P.E. CROUCH, and I. IGHNEIWA
12. Algebraic Riccati Equations Arising in Boundary/Point Control: A Review of Theoretical and Numerical Results Part I: Continuous Case ...................................................... 175 IRENA LASIECKA and ROBERTO TRIGGIANI
13. Algebraic Riccati Equations Arising in Boundary/Point Control: A Review of Theoretical and Numerical Results Part 11: Approximation Theory ........................................... 211 IRENA LASIECKA and ROBERTO TRIGGIANI
14. Some Control Problems for Time-Delay Systems ............. 236 V.M. MARCHENKO
15. Static and Dynamic Feedback Linearization ofNonlinear Systems................................................................................. 249 R. MARINO
16. Remarks on the Control of Discrete Time Nonlinear Systems ................................................................................. 261 HENK NIJMEIJER
17. Variational Problems Arising in Statistics ....................... 277 B.T. POLYAK
18. Necessary Conditions for an Extremum, Penalty Functions and Regularity ................................................... 286 BORIS N. PSHENICHNYJ
19. Transformations and Representations of Nonlinear Systems. ................................................................................ 297 A.J. VAN DER SCHAFT
ix
20. Why Real Analyticity is Important in Control Theory .... 315 H.J. SUSSMANN
21. Some Problems Arising in Connection with the Theory of Optimization ......................................................................... 341 V.M. TIKHOMIROV
List of Invited Speakers
Dirk Aeyels, University of Gent
Jozsef Bokor, Hungarian Academy of Sciences
Hector O. Fattorini, University of California
Michel Fliess, Ecole Superieure d'Electricite
Matheus L.J. Hautus, Eindhoven University of Technology
D. Hinrichsen, University of Bremen
Alexander D. Ioffe, Technion*
Velimir Jurdjevic, University of Toronto
Karl Kunisch, Technische Universität Graz
I.A.K. Kupka, University of Toronto
A.B. Kurzhanski, I.I.A.S.A.
F. Lamnabhi-Lagarrique, Ecole Superieure d'Electricite
lrena Lasiecka, University of Virginia
W.M. Marchenko, Kirov Byelorussian Institute of Technology
Riccardo Marino, Seconda Universita di Roma
Henk Nijmeijer, University of Twente
B.T. Polyak, Institute of Control Problems, Moscow
Boris N. Pshenichnyj, Academy of Sciences of the Ukrainian S.S.R.
A.J. van der Schaft, University of Twente
Hector J. Sussmann, Rutgers University
V.M. Tikhomirov, Moscow State University
* Contribution not received
Addresses of Contributors
Dirk Aeyels
Jozsef Bokor
Peter E. Crouch
Hector O. Fattorini
Michel Fliess
A.H.W. Geerts
Matheus L.J. Hautus
D. Hinrichsen
Department of Systems Dynamics University of Gent Grotesteenweg Nord 2, 9710 Gent, Belgium
Computer and Automation Institute Hungarian Academy of Sciences Kende U. 13-17, P.O. Box 63 H-1502 Budapest, Hungary
Department of Electrical and Computer Engineering Arizona State University Tempe, Arizona 85287, U.S.A.
Department of Mathematics University of California Los Angeles, California 90024, U.S.A.
Laboratoire des Signaux et Systemes Ecole Superieure d'Electricite Plateau du Moulon 91190 Gif-sur-Yvette, France
Department of Mathematics and Computing Science Eindhoven University of Technology 5600 MB Eindhoven, The Netherlands
Department of Mathematics and Computing Science Eindhoven University of Technology 5600 MB Eindhoven, the N etherlands
Institute for Dynamical Systems University of Bremen D-2800 Bremen 33, FRG
I. Ighneiwa
Velimir Jurdjevic
L. Keviczky
Karl Kunisch
I.A.K. Kupka
A.B. Kurzhanski
xii
Department of Electrical and Computer Engineering Arizona State University Tempe, Arizona 85287, U.S.A.
Department of Mathematics University of Toronto Toronto, M5S lAI Canada
Computer and Automation Institute Hungarian Academy of Sciences Kende U. 13-17, P.O. Box 63 H-1502 Budapest, Hungary
Institut für Mathematik Technische Universität Graz Kopernikusgasse 24, A-80l0 Graz, Austria
Department of Mathematics University of Toronto Toronto, M5S lAI Canada
International Institute for Applied Systems Analysis A-236l Laxenburg, Austria and Institute of Mathematics and Mechanics Sverdlovsk, U.S.S.R.
F. Lamnabhi-Lagarrique Laboratoi!"e des Signaux et Systemes Ecole Superieure d'Electricite Plateau du Moulon
Irena Lasiecka
W.M. Marchenko
Riccardo Marino
Henk Nijmeijer
91190 Gif-sur-Yvette, France
Department of Applied Mathematics University of Virginia Charlottesville, Virginia 22903, U.S.A.
Department of Mathematics Kirov Byelorussian Institute of Technology Swierdlova l3a, 200630 Minsk, U.S.S.R.
Dipartimento di Ingegneria Elettronica Seconda Universita di Roma Via Orazio Raimondo, 00173 Roma, Italia
Department of Applied Mathematics University of Twente, P.O. Box 217 7500 AE Enschede, the Netherlands
0.1. Nikonov
B.T. Polyak
A.J. Pritchard
Boris N. Pshenichnyj
A.J. van der Schaft
Hector J. Sussmann
V.M. Tikhomirov
Roberto Triggiani
xili
International Institute for Applied Systems Analysis A-2361 Laxenburg, Austria and Institute of Mathematics and Mechanies Sverdlovsk, U.S.S.R.
Institute of Control Problems Profsojuznaja 65 117-342 Moscow, B279, U.S.S.R.
Control Theory Centre, University of Warwick Coventry, England
Institute of Cybernetics Academy of Sciences of the Ukrainian S.S.R. Prospiekt 40-letija Oktiabria 142/144 25-2207 Kiev 207, U.S.S.R.
Department of Applied Mathematics University of Twente, P.O. Box 217 7500 AE Enschede, the Netherlands
Department of Mathematics Rutgers University New Brunswick, New Jersey 08903, U.S.A.
Department of Mathematics and Mechanies Moscow State University Leninskije Gory 117-234 Moscow, U.S.S.R.
Department of Applied Mathematics University of Virginia Charlottesville, Virginia 22903, U.S.A.