Table Of ContentISNM
International Series of Numerical Mathematics
Vol. 126
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 Vorau (Austria), July 14-20, 1996
Edited by
w.
Desch
F. Kappel
K. Kunisch
Springer Basel AG
Editors:
W. Deseh, F. Kappel and K. Kuniseh
Universitat Graz
Institut fiir Mathematik
Heinriehstra8e 36
A-8010 Graz
e-mails:[email protected]
[email protected]
[email protected]
1991 Mathematies Subjeet Classification 93-06, 49-06, 35-06
Library of Congress Cataloging-in-Publieation Data
Control and estimation of distributed parameter systems :
international eonferenee in Vorau (Austria), July 14-20, 1996/ edited by W. Deseh, F. Kappel, K. Kuniseh.
p. em. - (International series of numerical mathematies ; voI. 126)
Papers from the International Conference on Control and Estimation of Distributed Parameter Systems held
July 14-20, 1996, in Vorau, Austria.
Includes bibliographical references.
ISBN 978-3-0348-9800-3 ISBN 978-3-0348-8849-3 (eBook)
DOI 10.1007/978-3-0348-8849-3
1. Control theory - Congresses. 2. Distributed parameter systems - Congresses. 3. Estimation theory - Congresses.
1. Desch, W. (Wolfgang), 1953- II. Kappel. F. III. Kunisch, K. (Karl). 1952- IV. International
Conference on Control and Estimation of Distributed Parameter Systems (1996: Vorau, Styria, Austria)
V. Series: International series of numerical mathematics; V. 126.
QA402.3.C6262 1998
003',78-dc21
Deutsche Bibliothek Cataloging-in-Publication Data
Control and estimation of distributed parameter systems :
international conference in Vorau (Austria), July 14-20, 1996/ ed.
by W. Desch ... - Basel ; Boston; Berlin: Birkhiiuser, 1998
(International series of numerical mathematics ; VoI. 126)
ISBN 978-3-0348-9800-3
This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned,
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© 1998 Springer Basel AG
Originally published by Birkhiiuser Verlag,Basel, Switzerland in 1998
Softcover reprint ofthe hardcover Ist edition 1998
Printed on acid-free paper produced of chlorine-free pulp. TCF =
Cover design: Heinz Hiltbrunner, Basel
ISBN 978-3-0348-9800-3
987654321
Preface
TheInternationalConferenceon Control and EstimationofDistributed Parameter
Systemstookplacefrom July14-20, 1996, attheBildungshausChorherrenstiftVorau
in Vorau (Austria). It was the seventh in a series ofconferences that begun in 1982.
51 researchers from 11 states contributed to draw a broad and diverse picture of
the recent developments in optimal control and parameter identification of partial
differential equations, both from a theoretical and numerical viewpoint. We thank
them all for their contributions to an enjoyable and interesting conference.
We address our thanks to the whole staff of the Bildungshaus Chorherrenstift
Vorau. The pleasant atmosphere at the Bildungshaus has been a key ingredient to
the success ofthe meeting and the stimulating interaction between the participants.
We are particularly indebted to Mrs. L. ReiB, who helped us omnipresently with all
the everyday issues ofa conference like this one.
This meeting was facilitated by funding from the following organizations:
Amt der Steiermiirkischen Landesregierung,
Bundesministerium fUr Wissenschaft und Verkehr,
Christian Doppler Laboratorium fiir Parameter Identifikation
und Inverse Probleme,
European Research Office ofthe U.S. Army,
Spezialforschungsbereich F003 "Optimierung und Kontrolle",
Stadt Graz,
U.S. Air Force European Office ofAerospace Research and Development.
It is our pleasure to acknowledge the generous support by these institutions.
Once again, the friendly and supportive team of Birkhiiuser, in particular
Dr. T. Hintermann and Mrs. S. Lotrovsky, have provided an optimal opportunity
to publish our proceedings. Our special thanks go to Mrs. G. Krois. Herenthusiasm,
skillandworkpower havebeenthe backboneoftheorganizationoftheconferenceand
the preparation ofthe 'lEX manuscript ofthe proceedings you are presently reading.
Graz, July 1997
W. Desch, F. Kappel, K. Kunisch
List ofParticipants
H. T. BANKS North Carolina State University
M. BERGOUNIOUX Universite d'Orleans
F. BONNANS INRIA
A. BRIANI Universitadi Pisa
M. BROKATE Universitat Kiel
J. A. BURNS Virginia Tech
P. CANNARSA Universitadi Roma "Tor Vergata"
S. J. COX Rice University
W. DESCH Karl-Franzens-UniversiUit Graz
H. EGGHART US Army European Research Office
M. FALCONE Universita di Roma "La Sapienza"
H. O. FATTORINI University ofCalifornia
E. FERNANDEZ-CARA Universidad de Sevilla
A. V. FURSIKOV Moscow State University
J. HASLINGER KFK MFF UK
M. HEINKENSCHLOSS Rice University
M. HINZE TU Berlin
K. ITO North Carolina State University
F. KAPPEL Karl-Franzens-Universitat Graz
A. KAUFFMANN TU Berlin
C. T. KELLEY North Carolina State University
V. KOMORNIK Universite Louis Pasteur
M. KROLLER Karl-Franzens-Universitat Graz
K. KUNISCH Karl-Franzens-Universitat Graz
A. V. KUNTSEVICH Academy ofSciences ofthe Ukraine
G. LEUGERING Universitat Bayreuth
J. MALINEN Helsinki University ofTechnology
S. MICU Universidad Complutense de Madrid
viii ListofParticipants
F. MIGNOT Universite de Paris-Sud
B. S. MORDUKHOVICH Wayne State University
G. PEICHL Karl-Franzens-Universitat Graz
W. PRAGER Karl-Franzens-Universitat Graz
G. PROPST Karl-Franzens-Universitat Graz
J.-P. PUEL CMAP
A.M. RAMOS Universidad Complutense de Madrid
J.-P. RAYMOND Universite Paul Sabatier
W. RING Karl-Franzens-Universitat Graz
A. ROSCH TU Chemnitz-Zwickau
T. SLAWIG TU Berlin
R. C. SMITH Iowa State University
O. J. STAFFANS Abo Akademi University
D. TATARU Princeton University
M. E. TESSITORE Universita di Roma "Tor Vergata"
S. THALLER Karl-Franzcns-Univcrsitat Graz
R. TICHATSCHKE Univcrsitat Tricr
M. TUCSNAK CMAP
J. TURI University ofTexas at Dallas
C. WANG University ofSouthern California
J.-P. YVON Universite de Technologic de Compiegne
BING-Yu ZHANG University of Cincinnati
E. ZUAZUA Universidad Complutcnsc dc Madrid
Contents
H. T. BANKS AND G. A. PINTER:
Approximation results for parameter estimation
in nonlinear elastomers 1
A. BATTERMANN AND M. HEINKENSCHLOSS:
Preconditioners for Karush-Kuhn-Thcker matrices arising
in the optimal control ofdistributed systems 15
M. BERGOUNIOUX AND K. KUNISCH:
Augmented Lagrangian algorithms for state constrained
optimal control problems 33
A. BRIANI AND M. FALCONE:
A priori estimates for the approximation ofa parabolic
boundary control problem 49
M. BROKATE AND P. KREJCI:
On the wellposedness ofthe Chaboche model 67
P. CANNARSA AND M. E. TESSITORE:
On the behaviour ofthe value function ofa Mayer optimal
control problem along optimal trajectories 81
E. CASAS, J.-P. RAYMOND, AND H. ZIDANI:
Optimal control problem governed by semilinear elliptic
equations with integral control constraints and pointwise
state constraints 89
S. J. Cox:
Designing for optimal energy absorption II,
The damped wave equation 103
J. I. DiAZ AND A. M. RAMOS:
On the approximate controllability for higher order
parabolic nonlinear equations of Cahn-Hilliard type III
H. O. FATTORINI:
Control problems for parabolic equations with state
constraints and unbounded control sets 129
x Contents
E. FERNANDEZ-CARA AND J. REAL:
Remarks on the controllability ofsome stochastic partial
differential equations 141
K. ITO AND S. S. RAVINDRAN:
A reduced basis method for control problems governed
by PDEs 153
A. KAPLAN AND R. TICHATSCHKE:
Proximal penalty method for ill-posed parabolic optimal
control problems 169
V. KOMORNIK, P. LORETI, AND E. ZUAZUA:
On the control ofcoupled linear systems 183
G. LEUGERING:
On dynamic domain decomposition ofcontrolled networks
ofelastic strings and joint-masses 191
S. MICU AND E. ZUAZUA:
On a weakly damped system arising in the control of noise 207
B. S. MORDUKHOVICH AND KAIXIA ZHANG:
Dirichlet boundary control of parabolic systems with
pointwise state constraints 223
A. ROSCH:
Second order optimality conditions and stability estimates
for the identification of nonlinear heat transfer laws 237
R. C. H. DEL ROSARIO AND R. C. SMITH:
LQR control ofshell vibrations via piezoceramic actuators 247
O. J. STAFFANS:
The algebraic Riccati equation in discrete and
continuous time 267
D. TATARU:
The wave equation with Neuman controls:
On Lions's F-spacc 279
M. TUCSNAK:
On the pointwise stabilization ofa string 287
BING-Yu ZHANG:
Exact controllability ofthe generalized Boussinesq Equation 297
Approximation Results for Parameter Estimation
in Nonlinear Elastomers
H.T. BANKS AND GABRIELLA A. PINTER
Center for Research in Scientific Computation
North Carolina State University
Department ofMathematics
Texas Tech University
ABSTRACT. In this paper wepresent an approximationframework and theoreticalconver
gence results for a class of parameter estimation problems for general abstract nonlinear
hyperbolicsystems. Thesesystemsincludeasaspecialcasethosemodelinga largeclassof
nonlinearelastomers.
1991 Mathematics Subject Classification. 35R30
Keywordsandphmses. Abstractnonlinearhyperbolicsystems, parameterestimation,finite
dimensionalapproximation.
1. Introduction
Weconsiderthefollowing classofabstract nonlineardamped parameterdependent
hyperbolic systems evolving in a complex separable Hilbert space H:
(1.1) Wtt +AI(q)w+A2(q)wt +N*g(q)(Nw) = f(t; q)
(1.2) w(O) = 'Po
(1.3) Wt(O) = 'Pl'
Here AI(q),A2(q) are unbounded operators depending on some parameter q, g(q) is
a parameter dependent nonlinear operator in H, N is an unbounded operator, and
f is a parameter dependent forcing term. Precise conditions on these operators are
given below.
This class of systems was introduced in [BGS, BLMYj and further studied in
[BLGMY] as a model for the behavior of nonlinear elastomers. These materials,
which are used in the development of active and passive vibration devices, are rub
ber or polymer based composites that involve complex viscoelastic materials. Their
behaviorcannot be adequately modelled using the theory oflinearelasticity. Indeed,
they exhibit nonlinearities in material and geometric properties so that there is a
nonlinear relationship between stress and strain even for small strains. We illustrate
with a simple example that takes into account these nonlinearities, and describe the
associated general parameter estimation problems. (For detailed discussions of this
and other models see [BLMY, BGS, BLGMY, B1].)
W. Desch et al. (eds.), Control and Estimation of Distributed Parameter Systems
© Springer Basel AG 1998
