Optimal Control of Distributed Systems with Conjugation Conditions
This work develops the methodology according to which classes of discontinuous functions are used in order to investigate a correctness of boundary-value and initial boundary-value problems for the cases with elliptic, parabolic, pseudoparabolic, hyperbol
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Nonconvex Optimization and Its Applications Volume 75 Managing Editor: Panos Pardalos University of Florida, USA. Advisory Board: J. R. Birge University of Michigan, USA. Ding-Zhu Du University of Minnesota, U.S.A. C. A. Floudas Princeton University, USA. J. Mockus Lithuanian Academy of Sciences, Lithuania H. D. Sherali Virginia Polytechnic Institute and State University, USA. G. Stavroulakis Technical University Braunschweig, Germany H. Tuy National Centre for Natural Science and Technology, Vietnam
OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS WITH CONJUGATION CONDITIONS By IVAN V. SERGIENKO Glushkov Institute of Cybernetics, Ukraine VASYL S. DEINEKA Glushkov Institute of Cybernetics, Ukraine
Editor NAUM Z. SHOR National Academy of Science of Ukraine
Kluwer Academic Publishers
Library of Congress Cataloging-in-Publication Data A C.I.P. record for this book is available from the Library of Congress.
ISBN 1-4020-8108 -1
e-ISBN 0-387-24256-2
Printed on acid-free paper.
© 2005 Kluwer Academic Publishers
All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 987654321 springeronline.com
SPIN 11161936
CONTENTS
PREFACE 1
xi
CONTROL OF SYSTEMS DESCRIBED BY ELLIPTIC-TYPE PARTIAL-DIFFERENTIAL EQUATIONS UNDER CONJUGATION CONDITIONS 1.1 1.2 1.3 1.4 1.5 1.6 1.7
Distributed Control of a System Described by the Dirichlet Problem Control Under Conjugation Condition. The Dirichlet Problem Boundary Control of a Correct System Described by the Neumann Problem Distributed Control of a System: A Complicated Thin Inclusion Case Control Under Conjugation Condition: A Complicated Thin Inclusion Case Boundary Control: Third Boundary-Value Problem Boundary Control and Observation: Third Boundary-Value Problem
1
1 13 21 30 41 49 57
VI
CONTROL OF A CONDITIONALLY CORRECT SYSTEM DESCRIBED BY THE NEUMANN PROBLEM FOR AN ELLIPTIC-TYPE EQUATION UNDER CONJUGATION CONDITIONS 63 2.1 2.2 2.3 2.4 2.5
Distributed Control with Observation throughout a Whole Domain Distributed Control with Observation on a Thin Inclusion Distributed Control with Boundary Observation Control under Conjugation Condition with Boundary Observation Boundary Control with Observation on a Thin Inclusion
CONTROL OF A SYSTEM DESCRIBED BY A ONE-DIMENSIONAL QUARTIC EQUATION UNDER CONJUGATION CONDITIONS 3.1 3.2 3.3 3.4 3.5
Distributed Control with Observation thro
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