Optimal Control Theory, Algorithms, and Applications
February 27 - March 1, 1997, the conference Optimal Control: The ory, Algorithms, and Applications took place at the University of Florida, hosted by the Center for Applied Optimization. The conference brought together researchers from universities, indu
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Applied Optimization Volume 15 Series Editors: Panos M. Pardalos University of Florida, U.S.A. Donald Hearn University of Florida, U.S.A.
The titles published in this series are listed at the end of this volume.
Optitnal Control Theory, Algorithms, and Applications
by
William H. Hager Department ofMathematics, University of Gainesville
and Panos M. Pardalos Department ofIndustrial & Systems Engineering, University ofFlorida, Gainesville
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication Data
ISBN 978-1-4419-4796-3 ISBN 978-1-4757-6095-8 (eBook) DOI 10.1007/978-1-4757-6095-8
Printed on acid-free paper
Ali Rights Reserved © 1998 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1998 No part ofthe material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
Contents Preface Uniform Decays in Nonlinear Thermoelastic Systems
xv
1
George Avalos and Irena Lasiecka 1 Introduction 1.1 Statement of the Problem 1.2 Statement of the Main Result 1.3 Abstract Formulation 2 Proof of Main Result References
2 2 4 6 13 22
Absolute Stability of Feedback Systems in Hilbert Spaces
24
Francesca Bucci 1 Introduction 2 The Convolution Equation Approach 3 Frequency Theorems with Application to Stability 4 Feedback Systems with Unbounded Input Operator References
25 27 30 35 36
A Projection Method for Accurate Computation of Design Sensitivities
40
John A. Burns, Lisa G. Stanley, and Dawn L. Stewart 1 Introduction 2 A Model Problem 2.1 The Sensitivity Equation
41 41 42
vi
2.2 Numerical Approximations 3 Computational Algorithms 3.1 A Finite Element Scheme 3.2 The Smoothing Projection Scheme 4 Numerical Results 4.1 Convergence of Solutions for the Boundary Value Problem and Sensitivity Equation 4.2 Optimization Results 5 A 2-D Flow Problem 5.1 Flow Around a Cylinder 5.2 Numerical Results 6 Conclusions and Future Work References
50 55 57 60 61 65 65
On Exact Controllability and Convergence of Optimal Controls to Exact Controls of Parabolic Equations
67
43 45 46 48 50
Yanzhao Gao, Max Gunzburger, and James Turner 1 Introduction 2 Definitions, Notation and Preliminaries 3 Representation of the Terminal State 3.1 An Operator Representation of the Terminal State 3.2 Properties of the Operator R 3.3 Approximate Controllability: a Constructive Proof 4 Exact Controllability and Convergence of the Optimal Controls to Exact Controls: A Constructive Proof of Exact Controllability
77
References
81
Spectral Analysis of Thermo-elastic Plates with Rotational Forces
84
S. K. Chang and Roberto Triggiani 1 Introduction. Problem Statement. Main Result 1.1 Motivation and Overview 1.2 Statement of Analyticity for r = 0
68 68 72 72 73 76
85 85 87
vii
1.3 Statement of Lack of Compactness and Differentiability for 1 > 0 1 2 Spectral Analysi
