A

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.