Boundary Control and Boundary Variation

Transcription

1 J.R Zol6sio (Ed.) Boundary Control and Boundary Variation Proceedings ofifip WG 7.2 Conference Sophia Antipolis, France, October 15-17, 1990 Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo HongKong Barcelona Budapest

2 Advisory Board L.D. Davisson-A.G.J. MacFarlane H. Kwakernaak J.L. Massey "Ya Z. Tsypkin" A. J. Viterbi Editor Jean Paul Zoldsio Institut Non Lindaire de Nice Universitd de Nice Sophia Antipolis Facultd des Sciences, B.P. No Nice Cedex 2, France and Cenlxe de Mathdmatiques Appliqudes Ecole des Mines, B.P Sophia Antipolis, France ISBN Springer-Verlag Berlin Heidelberg New York ISBN Springer-Verlag New York 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 of the 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. International Federation for Information Processing, Geneva, Switzerland, 1992 Printed in Germany The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of 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 60/ Printed on acid-free paper

3 PREFACE This volume comprises the proceedings of the Working Conference "Boundary Control and Boundary Variation" held in Sophia- Antipolis ( France ), october The conference was organized for the Working Group 7.2 (Computational methods for control systems described by partial differential equations) of Technical Committe 7 (Modelling and Optimization Techniques ) of the international Federation for Information Processing (IFIP). That conference was the fourth one organized in south of France and sponsored by the following French institutions : Centre National de la Recherche Scientifique (CNRS) Centre de Mathrmatiques Appliqures (CMA) in Sophia Antipolis A6rospatiale, Cannes-la-Bocca. These conferences were: - june 86 IFIP 7.2 in Nice, proc. "Boundary Variation and Boundary Control", L.N.C.I.S. Springer Veriag, no I00, december 87,COMCON conference in Montpellier, proc. "Stabilization of Flexible Structures",Optimization Softwarelnc.,L.A january 89 in Montpellier, proc. "Stabilization of Flexible Structure",L.N.C.I.S. Springer Verlag, no 147, october 90 IFIP 7.2 in Sophia-Antipolis, these proc. The aim of these conferences is to stimulate exchange of ideas between the group working on Shape Optimization (including free boundary problems) and the group working on boundary control of hyperbolic systems ( including Stabilization ). J was helped on the organizing committee by J.P. Marmorat, CMA J. Leblond, CMA & My thanks go to the 35 authors of the contributions contained in this volume. Sophia-Antipolis, july 1991 LP. Zolrsio

4 CONTENTS Andr6a-Novel, F. Boustany, E Conrad Control of An Overhead Crane : Stabilization of Flexibilities A. Bensoussan Exact Controllability For Linear Dynamic Systems With Skew Symmetric Operators A. Brillard Boundary Homogeneization and Boundary Shape Optimization for a Cylinder G. Buttazzo Relaxed Formulation For a Class of Shape Optimization Problems P. Cannarsa, F. Gozzi On the Smoothness of the Value Function Along Optimal Trajectories G. Chen, J. Zhou Some Boundary Control Problems and Computation For The Linear Elastotatic Kirchoff Plate On An Exterior Domain D. Cioranescu, P. Donato, E. Zuazua Approximate Controllability for Wave Equation With Oscillating Coefficients D. Cioranescu, J. Saint Jean-Paulin Truss Structures: Fourier Conditions and Eigenvalue Problem F. Conrad, J. Leblond, J.P. Marmorat Boundary Control and Stabilization of the One-dimensional Wave Equation G. Da Prato, J.P. Zol6sio Boundary Control for Inverse Free Boundary Problems M. Delfour, J. Morgan Differentiability of Min Max and Saddle Points under relaxed Assumptions M. Delfour, A. Ouansafi New Noniterative Approximations of the Old Riccati Diffemtial Equation

5 viii A. Eljendy Numerical Approach to the Exact Controllability of Hyperbolic Systems D.Gatarek, J. Sokolowski Shape Sensitivity Analysis for Stochastic Evolution Equations R. Glowinski Boundary Controllability Problems for the Wave and Heat Equations A. Henrot, M. Pierre About Critical Points of the Energy in an Electromagnetic Shaping Problem I. Lasiecka Finite Dimensional compensator for Flexible Structures W. Littman Remarks On Boundary Control For Polyhedral Domains And Related Results A. Lunardi Stability of the Travelling Waves in a Class of Free Boundary Problems Arising in a Combustion Theory J.P. Marmorat, G. Payre, J.P. Zolrsio A Convergent Finite Element Scheme for a Wave Equation with a Moving Boundary R. Makinen, P. Neittaanmaki, D. Tiba A Boundary Controllability Approach in Optimal Shape Design Problems R. Triggiani Regularity With Interior Point Control. Part I : Wave and Euler-Bemoulli Equations P. Villaggio, J.P. Zolrsio New Results in Shape Optimization. I.P. Zol6sio Shape Formulation of Free Boundary Problems With Non Linearized Bernoulli Condition