Optimal Control
There is an ever-growing interest in control problems today, con nected with the urgent problems of the effective use of natural resources, manpower, materials, and technology. When referring to the most important achievements of science and technology i
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CONTEMPORARY SOVIET MATHEMATICS Series Editor: Revaz Gamkrelidze, Steklov Institute, Moscow, USSR
COHOMOLOGY OF INFINITE-DIMENSIONAL LIE ALGEBRAS
D. B. Fuks DIFFERENTIAL GEOMETRY AND TOPOLOGY A. T. Fomenko LINEAR DIFFERENTIAL EQUATIONS OF PRINCIPAL TYPE
Yu. V. Egorov OPTIMAL CONTROL
V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin THEORY OF SOLITONS: The Inverse Scattering Method
S. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov
TOPICS IN MODERN MATHEMATICS: Petrovskii Seminar No.5 Edited by 0. A. Oleinik
Opt ima l Con trol V. M. Aleksee v V. M. Tikhom irov and S. V. Fomin Department of Mathematics and Mechanics Moscow State University Moscow, USSR
Translated from Russian by
V. M. Volosov
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging in Publication Data Alekseev, V. M. (Vladimir Mikhailovich) Optimal control. (Contemporary Soviet mathematics) 1. Control theory. 2. Mathematical optimization. I. Tikhomirov, V. M. II. Fomin, S. V. (Sergei Vasil'evich Ill. Title. IV. Series.
QA402.3.A14 1987 ISBN 978-1-4615-7553-5 DOI 10.1007/978-1-4615-7551-1
001.53 87-6935 ISBN 978-1-4615-7551-1 (eBook)
This translation is published under an agreement with the Copyright Agency of the USSR (VAAP) .
© 1987 Springer Science+Business Media New York Originally published by Plenum Publishing Corporation, New York in 1987 Softcover reprint of the hardcover 1st edition 1987 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher
PREFACE
There is an ever-growing interest in control problems today, connected with the urgent problems of the effective use of natural resources, manpower, materials, and technology. When referring to the most important achievements of science and technology in the 20th Century, one usually mentions the splitting of the atom, the exploration of space, and computer engineering. Achievements in control theory seem less spectacular when viewed against this background, but the applications of control theory are playing an important role in the development of modern civilization, and there is every reason to believe that this role will be even more significant in the future. Wherever there is active human participation, the problem arises of finding the best, or optimal, means of control. The demands of economics and technology have given birth to optimization problems which, in turn, have created new branches of mathematics. In the Forties, the investigation of problems of economics gave rise to a new branch of mathematical analysis called linear and convex programming. At that time, problems of controlling flying vehicles and technological processes of complex structures became important. A mathematical theory was formulated in the mid-Fifties known as optimal control theory. Here the maximum principle of L. S. Pontryagin played a pivotal role. Optimal control theo
