ISNM International Series of Numerical Mathematics Vol. 143 Managing Editors: K.-H. Hoffmann, Munchen D. Mittelmann, Tempe Associate Editors: R. E. Bank, La Jolla H. Kawarada, Chiba R. J. LeVeque, Seattle C. Verdi, Milano Honorary Editor: J.Todd,Pasadena Control and Estimation of Distributed Parameter Systems International Conference in Maria Trost (Austria), July 15-21, 2001 Edited by W. Desch F. Kappel K. Kunisch Springer Basel AG Editors: W. Desch. F. Kappel and K. Kunisch Universittil Oraz InstituI rur Mathematik HcinrichstraBe 36 8010 Graz Austria e-mails:[email protected] f [email protected] [email protected] 2000 Mathematies Subjeci Classification 35L05. 35Q72. 47006.49J40. 49K40. 49NOS. 62H30. 6SC20. 65M99. 65P99. 68U99. 76D05. 93A15. 93B07. 93C". 93DI5 A CIP eatalogue record for this book is available from the Library of Congrcss. Washington D.C .• USA Bibliographic informmion published by Die Dcutsche Bibliothek Die Dcutsche Bibliothek lists Ihis publication in Ihe Deutsche Nationalbibliografie: dctailcd bibliographic dala is available in the Internet al <hnp:/Idnb.ddb.de>. ISDN 978·3·0J~8·9399·2 This work is subjectlo copyright. AII righlS are reserved. whether Ihe whole or part of thc material is conccmcd. spe<:ifically thc rights of translation. reprinting. rc-use of iIIustr:uions. rccilation. broadcasting. rcproduction on microfilms or in olher ways. and Sloragc in d:ua banks. For any kind of use pcnnissioll of the copyright owncr must bc obtaincd. C 2003 Springer Base! AG Originally publishcd by BirkhAuscr Vcrlag Basel,Swilzerland in 2003 Sof"tcover reprint ofthe hardcover ISI edition 2003 Primed on acid-frec paper produced of chlorine-free pulp. TCF 00 ISBN 978-3-0348-9399-2 ISBN 978-3-0348-8001-5 (eBook) DOI 10.1007/9'78-3-0348-8001-5 987654321 www.birkhasucr-scicnce.com Contents Preface VII Participants ix H.T. Banks, S.C. Beeler, and H.T. Tran State Estimation and Tracking Control of Nonlinear Dynamical Systems 1 H.T. Banks, H. Tran, and S. Wynne A Well-posedness Result for a Shear Wave Propagation Model 25 R. Becker and B. Vexler Mesh Adaptation for Parameter Identification Problems 41 M. Bergounioux and M. Haddou A SQP-Augmented Lagrangian Method for Optimal Control of Semilinear Elliptic Variational Inequalities 57 J.A. Burns and J.R. Singler On the Long Time Behavior of Approximating Dynamical Systems 73 K. Deckelnick and M. Hinze Error Estimates in Space and Time for Tracking-type Control of the Instationary Stokes System 87 M.C. Delfour Modeling and Control of Asymptotic Shells 105 W. Desch, E. FaSanga, and J. Milota Unbounded Observers and Riccati Operators in Nonrefiexive Spaces 121 Q. Du and M. Gunzburger Centroidal Voronoi Tessellation Based Proper Orthogonal Decomposition Analysis 137 H.O. Fattorini Time and Norm Optimal Controls for Linear Parabolic Equations: Necessary and Sufficient Conditions 151 A. Fursikov Feedback Stabilization for the 2D Oseen Equations: Additional Remarks 169 VI Contents G. Grammel Pontryagin's Maximum Principle via Singular Perturbations 189 K. Ito Level Set Methods for Variational Problems and Applications 203 V. Komornik and P. Loreti Boundary Observability of Compactly Perturbed Systems 219 S. Manservisi Some Shape Optimal Control Computations for Navier-Stokes Flows 231 R.C. Smith and M.V. Salapaka Model Development for the Positioning Mechanisms in an Atomic Force Microscope 249 Preface This volume contains the Proceedings of the International Conference on Control of Distributed Parameter Systems, held in Graz (Austria) from July 15-21, 2001. It was the eighth in a series of conferences that began in 1982. Included are a broad variety of topics related to partial differential equations, ranging from abstract functional analytic framework to aspects of modelling, with the main emphasis, however, on theory and numerics of optimal control for nonlinear distributed pa rameter systems. 48 researchers from 11 countries attended the conference. We thank all of them for their lectures, their contributions to this volume, and many stimulating discussions. For the first time the conference took place in the Bildungshaus Mariatrost in Graz. We enjoyed a very pleasant and supportive environment. Our thanks go to the whole staff of the Bildungshaus Mariatrost for helping us with solving many everyday issues. This meeting was facilitated by funding from the following organizations: European Office of Aerospace Research and Development Air Force Office of Scientific Research United States Air Force Research Laboratory Karl-Franzens-Universitiit Graz Special Research Center on Optimization and Control Stadt Graz Steiermiirkische Landesregierung It is our pleasure to acknowledge the generous support by these institutions. We wish to thank the friendly team of Birkhiiuser for the enjoyable cooper ation, in particular Dr. T. Hintermann, Mrs. S. Lotrovsky, and Dr. T. Hempfling. It is Mrs. G. Krois who carried the main burden of coordinating the con ference and preparing these proceedings. We express our special thanks for her immense workpower and experience, and her everlasting encouragement and opti mism. Graz, July 2002 W. Desch, F. Kappel, K. Kunisch Participants H. T. Banks North Carolina State University, Raleigh, USA J. Batzel Karl-Franzens-Universitat Graz, Graz, Austria M. Bergounioux Universite d'Orleans, Orleans, France A. Borzi Karl-Franzens-Universitat Graz, Graz, Austria M. Brokate Technische Universitat Miinchen, Miinchen, Germany J.A. Burns Virginia Polytechnic Institute and State University, Blacksburg, USA P. Cannarsa Universita di Roma "Tor Vergata", Roma, Italy M.C. Delfour Universite de Montreal, Montreal, Canada W. Desch Karl-Franzens-Universitat Graz, Graz, Austria J.C. DelosReyes Karl-Franzens-Universitat Graz, Graz, Austria E. FaSanga Charles University, Praha, Czech Republic H.O. Fattorini University of California, Los Angeles, USA M. Fink Karl-Franzens-Universitat Graz, Graz, Austria A.V. Fursikov Moscow State University, Moscow, Russia G. Grammel Technische Universitat Miinchen, Miinchen, Germany M.D. Gunzburger Iowa State University, Ames, USA J. Haslinger Charles University, Praha, Czech Republic M. Heinkenschloss Rice University, Houston, USA M. Hintermiiller Karl-Franzens-Universitat Graz, Graz, Austria M. Hinze Technische Universitat Dresden, Dresden, Germany A. Ignat Karl-Franzens-Universitat Graz, Graz, Austria K. Ito North Carolina State University, Raleigh, USA F. Kappel Karl-Franzens-Universitat Graz, Graz, Austria S. Keeling Karl-Franzens-Universitat Graz, Graz, Austria V. Komornik Universite Louis Pasteur, Strasbourg, France P. KrejCi Czech Academy of Sciences, Praha, Czech Republic K. Kunisch Karl-Franzens-Universitat Graz, Graz, Austria A. Kunoth Universitat Bonn, Bonn, Germany P. Loreti Universita di Roma "La Sapienza", Roma, Italy S. Manservisi Universita di Bologna, Bologna, Italy S. Micu Universidad Complutense, Madrid, Spain J. Milota Charles University, Praha, Czech Republic G. Peichl Karl-Franzens-Universitat Graz, Graz, Austria G. Propst Karl-Franzens-Universitat Graz, Graz, Austria J. Priiss Martin-Luther Universitat Halle-Wittenberg, Halle, Germany x Participants J.-P. Raymond Universite Paul Sabatier, Toulouse, France W. Ring Karl-Franzens-Universitiit Graz, Graz, Austria R.C. Smith North Carolina State University, Raleigh, USA U. Spassov University Rovira i Virgili, Tarragona, Spain H.T. Tran North Carolina State University, Raleigh, USA F. Troltzsch Technische Universitiit Berlin, Berlin, Germany M. Tucsnak Universite de Nancy I, Vandoeuvre les Nancy, France M. Ulbrich Technische Universitiit Munchen, Munchen, Germany S. Ulbrich Technische Universitiit Munchen, Munchen, Germany B. Vexler Universitiit Heidelberg, Heidelberg, Germany S. Volkwein Karl-Franzens-Universitiit Graz, Graz, Austria G. Weiss Imperial College of Science and Technology, London, United Kingdom H. J. Zwart Universiteit Twente, Enschede, The Netherlands