Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems: Proceedings of the 10th International Conference Sophia-Antipolis, France, June 9–12, 1992 PDF
Preview Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems: Proceedings of the 10th International Conference Sophia-Antipolis, France, June 9–12, 1992
Lecture Notes in Control and Information Sciences 185 Editors: M. Thoma and W. Wyner R.E Curtain (Editor) A. Bensoussan, J.L. Lions (HonoraryE ds.) Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite- Dimensional Systems Proceedings of the 10th Intemational Conference Sophia-Antipolis, France, June 9-12, 1992 Springer-Verlag Berlin Heidelberg New York London Paris Tokyo HongKong Barcelona Budapest Advisory Board L.D. Davisson • A.GJ. MacFarlane. H. Kwakemaak J.L. Massey-Ya Z. Tsypkin "A.J. Viterbi Editor R.F. Curtain University o f Groningen The Netherlands Honorary Editors A. Bensoussan INRIA - Universit~ Paris IX Dauphine L Lions Collage de France - CNES, Paris INRIA Institut National de Recherche en Informatique et en Automatique Domaine de Voluceau, Rocquencourt, B.P. 105 78153 Le Chesnay, France ISBN 3-540-56155-2 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-387-56155-2 Springer-Verlag NewYork Berlin Heidelberg This Work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions ofthe German Copyright Law of September 9, 1965, in its current version and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1993 Printed in Germany The use of registered names, trademarks, etc. in this publication does not imply, even in the absence e r a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera ready by authors Offsetprinting: Mercedes-Druck, Berlin; Bookbinding: B. Hell , Berlin 61/3020 5 4 3 2 1 0 Printed on acid-free paper F O R E W O R D The 10th Conference on "Analysis and Optimisation of Systems" organised by INRIA is marked by a change in form : instead of covering a wide range of topics, as in the past, this conference is devoted to a specific domain of the theory of infinite- dimensional systems.We plan to proceed in the same way in the future, and we will cover the whole field of Analysis and Optimisation of Systems by a series of specialized conferences. Among the advantages, this allows the possibility of covering a specific area in more depth and it gives the participants more opportunity for fruitful interaction. We would like to express our thanks to the Organizations which have sponsored this Conference: DRET and ONREUR We also would like to extend our gratitude to : - the authors who have shown an active participation in this Conference - the many reviewers who have accepted the difficult task of selecting papers - the chairpersons for having run with efficiency all the sessions of the Conference - all the members of the Organization Committee, and particularly Ruth Curtain who did a wonderful job. - The Public Relations Departement of INRIA and particulary C. Genest and F. Tapissier for their excellent work in making this Conference really happen. - Professor M. THOMA and the Editor SPRINGER VERLAG who have accepted to publish this series in the Lecture Notes in Control and Information Sciences. A. Bensoussan J.L. Lions This conference is under the sponsorship of: DRET Direction des Recherches Etudes et Techniques ONREUR Office of US Naval Research in Europe INTERNATIONAL PROGRAMME COMMI'I"rEE Chairperson R. CURTAIN University of Groningen / INRIA-Rocquencourt J. BALL Virginia University, USA J. BARAS University of Maryland, USA L. BARATCHART INRIA-Sophia, France J. BLUM Universit6 de Grenoble, France F. CALLIER Dept. Math.FUNDP, Namur, Belgium G. Da PRATO Scuola Normale Superiore, Pisa, Italy M. DELFOUR Centre de Recherches Math.,Montr6al, Canada P. GAHINET INRIA-Rocquencourt, France W. KRABS Techn. Hochschule Darmstadt, Germany A.J. PRITCHARD University of Warwick, UK M. SORINE INRIA-Rocquencourt, France J.P. YVON INRIA-Rocquencourt / Universit6 de Technologic de Compi6gne, France J. ZABCZYK Institute of Mathematics, Warsaw, Poland LOCAL ORGANIZING COMI'I"rEE L. BARATCHART INRIA-Sophia, France J. BLUM Universitd de Grenoble, France P. GAHINET INRIA-Roequencourt, France M. SORINE INRIA-Roequencourt, France J.P. YVON INRIA-Rocquencourt / Universitd de Technologic de Compi~gne, France CONFERENCE SECRETARIAT C. GENEST INRIA-Rocquencourt, France F. TAPISSIER INRIA-Rocquencourt, France INTRODUCTION The aim of the conference was to bring together engineers and mathematicians working in the field of infinite-dimensional systems who are specialists in one or more of the following categories of mathematical approaches : _ semi-group approaches _ partial differencial approaches _ frequency domain approaches _ synthesis of state and frequency domain approaches Since these approaches use very different sophisticated mathematical techniques, it is unusual for a scientist to be expert in all of them. On the other hand, these different approaches all purport to address the same control problems for the same classes of linear infinite-dimensional systems. It is therefore important to compare and discuss the advantages and disadvantages of these different mathematical techniques. To help ameliorate the communication gap a series of introductory tutorial lectures were given by specialists in above-mentionned fields. The writter accounts of these introductory lectures, together with their references, form an extremely useful source of background information on a very wide class of problems and approaches in linear infinite-dimensional sys tems . For example, the semi-group theme is represented by an article on general background, an up-to*date survey on the Linear Quadratic Control Problem and Riceati equations and an account of the state-space approach to HOO-optimal control problem. The results on this last very recent topic are less maticre than those on the Linear Quadratic Control Problem, but since the techniques involved are very similar a strong interaction between these two domains of activity can be expected in the future. Indeed,. it has already begun. The second theme concerns input-output descriptions of systems in terms of transfer functions.After an introductory article on transfer functions, an outline of the coprime factorisation approach to control synthesis for different classes of transfer functions follows. The final paper on this theme concerns the application of these techniques to the important problem of robust controller design and in particular, finite-dimensional controller design in these articles, the connections with the first theme (semi-group approach) arc emphasized. The third theme on partial differential equations is also introduced with a background article on the Lions approach, followed by recent results on Exact Controllability and Stabilisation using both the Hilbert Uniqueress Method and high frequency asymptotic methods. The last theme on frequency domain approaches is also based on a transfer function description, but the connections with a state-space representation are not relevant.The first article describes the utilization of classical ideas in Harmonic Analysis, such as Hank¢l operators and Nehari's Theorem, to the systems theory context. Robust controller design is treated in a more general and deeper context in the second article and the final contribution to this theme surveys recent results on the same HOO-domain viewpoint using techniques from Harmonic Analysis. In addition, the proceedings contains several key survey papers on fundamental topics such as geometric theory, robust stability radii and relationships between input- output stability and exponential stability. Last, but not least, the proceedings contains many shorter contributions on recent original research covering all four of the above- mentionncd themes. VII I Of course, bringing together scientist from four very different approaches with the aim of having them interact with each other is an ambitious one. In this we succeeded, especially during the final round table discussion on "Different Approaches to Control of Infinite-Dimensional Linear Systems". The aim of these proceedings is to help to promote further interaction and fruiful collaboration in the future between scientists working on different approaches to the challenging problems in the field of infinite-dimensional linear systems. T A B L E O F C O N T E N T S 1. T U T O R I A L L E C T U R E S S E M I - G R O U P A P P R O A C H Introduct ion to Semigroup Theory A. J. PRITCHARD ................................................................................................... Riccati Equations Arising from Boundary and Point Control Problems I. LASIECKA ............................................................................................................ 23 A State-Space Approach to the H**-Control Problems for I n f i n i t e - D i m e n s i o n a l Sys t ems B. VAN KEULEN ..................................................................................................... 46 SYNTHESIS OF STATE AND F R E Q U E N C Y DOMAIN A P P R O A C H E S Infini te Dimensional System Transfer Funct ions F. M. CALLIER, J . WINKIN ............................................................................... 72 Stabi l izat ion and Regulat ion of Inf in i te-Dimensional Systems Using Copr ime Factor izat ions H. LOGEMANN ......................................................................................................... 102 Robust Control lers for Inf in i te -Dimensional Systems R. F. CURTAIN ......................................................................................................... 140 P A R T I A L D I F F E R E N T I A L E Q U A T I O N A P P R O A C H E S Control for Hyperbol ic Equations G. LEBEAU ................................................................................................................. 160 An Introduction to the Hilbert Uniqueness Method A. BENSOUSSAN ........................................................................................................ 184 F R E Q U E N C Y DOMAIN A P P R O A C H E S The Nehari Problem and Optimal Hankel Norm Approximation N. J. YOUNG ............................................................................................................. 199 Topological Approaches to Robutness T.T. G E O R G I O U , M. C. SMITH ............................................................................. 222 Frequency Domain Methods for the H**-Optimization of Distr ibuted Systems A. T A N N E N B A U M .................................................................................................... 242 X 2. CONTRIBUTED PAPERS SEMI-GROUP APPROACH Disturbance Decoupling Problem for Infinite-Dimensional Systems H. J. ZWART .............................................................................................................. 279 Simultaneous Triangular-Decoupling, Disturbance-Rejection and Stabilization Problem for Infinite-Dimensional Systems N. OTSUKA, H. INABA, K. TORAICHI ............................................................. 290 Robust Stability Radii for Distributed Parameter Systems : A Survey S. TOWNLEY ............................................................................................................... 302 Solutions of the ARE in terms of the Hamiltonian for Riesz-spectral Systems C. R. KUIPER, H. J. ZWART ............................................................................... 314 Regional Controllability of Distributed Systems A. EL JAI, A. J. PRITCHARD ............................................................................. 326 On Filtering of the Hilbert Space-valued Stochastic Process over Discrete-continuous Observations Y. V. ORLOV, M. V. BASIN ................................................................................... 336 Boundary Stabilization of Rotating Flexible Systems C. Z. XU, G. SALLET ................................................................................................ 347 SYNTHESIS OF STATE AND FREQUENCY DOMAIN APPROACHES Frequency Domain Methods for Proving the Uniform Stability of Vibrating Systems R. REBARBER .......................................................................................................... 366 The Well-Posedness of Acceleromctcr Control Systems K. A. MORRIS .......................................................................................................... 378 Comparison of Robustly Stabilizing Controllers for a Flexible Beam Model with Additive, Multiplicative and Stable Factor Perturbations J.B O N T S E M A , R . F . C U R T A I N , C . R . K U I P E R , H . M . O S I N G A. ........................... 388 On the Stability Uniformity of Infinite-Dimensional Systems H. ZWART, Y. YAMAMOTO, Y. GOTOH ............................................................ 401 ×l PARTIAL DIFFERENTIAL EQUATION APPROACHES High Frequency Asymptotic Approach for Incomplete Spectral and Local Controllability C. BARDOS .................................................................................................................. 410 Modelling and Controllability of Plate-Beam Systems J. E. LAGNESE .......................................................................................................... 423 A Simple Viscoelastic Damper Model - Application to a Vibrating String G. MONTSENY, J. AUDOUNET, B. MBODJE .................................................... 436 Controllability of a Rotating Beam W. KRABS .................................................................................................................. 447 Min-Max Game Theory for a Class of Boundary Control Problems C. MCMILLAN, R. TRIGGIANI ......................................................................... 459 Microlocal Methods in the Analysis of the Boundary Element Method M. PEDERSEN ........................................................................................................... 467 Stochastic Control Approach to the Control of a Forward Parabolic Equation, Reciprocal Process and Minimum Entropy A. BLAQUIERE, M. SIGAL-PAUCHARD ......................................................... 476 Observability of Hyperbolic Systems with Interior Moving Sensors A. KHAPALOV .......................................................................................................... 489 Controllability of a Multi-Dimensional System of Schr0dinger Equations : Application to a System of Plate and Beam Equations J. P. PUEL, E. ZU A Z U A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 Decay of Solutions of the Wave Equation with Nonlinear Boundary Feedback F. CONRAD, B. RAO ................................................................................................ 512 Boundary Approximate Controllability for Semilinear Heat Equations C. FABRE, J. P. PUEL, E. ZUAZUA ................................................................... 524 On the Stabilization of the Wave Equation O. MORGUL ................................................................................................................ 531 FREQUENCY DOMAIN APPROACHES The Hankel Singular Values of a Distributed Delay Line A Fredholm Equation Approach L. PANDOLFI ............................................................................................................ 543 Rational Approximation of the Transfer Function of a Viscoelastic Rod K. B. HANNSGEN, R. L. WHEELER, O. J. STAFFANS ................................ 551 Some Extremal Problems linked with Identification from Partial Frequency Data D. ALPAY, L. BARATCHART, J. LEBLOND ................................................... 563
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