Numerical Methods for Optimal Control Problems with State Constraints
While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new me
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1707
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Radoslaw Pytlak
Numerical Methods for Optimal Control Problems with State Constraints
Springer
Author Rados,taw Pytlak Faculty of Cybernetics Military University of Technology ul. Kaliskiego 2 01-489 Warsaw, Poland E-maih rpytlak @ isi.wat.waw.pl
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Pytlak, R., 1956N u m e r i c a l methods For o p t i m a l c o n t r o l problems w i t h s t a t e c o n s t r a i n t s / R. P y t l a k . p. ca. - - ( L e c t u r e notes In mathematics; 1707) Includes bibliographical r e f e r e n c e s and lndex. ISBN 3-540-66214-6 (elk. paper) 1. Control theory. 2. Mathematical optimization. 3. N u m e r i c a l analysis. I. Title. I I . S e r t e s : L e c t u r e notes In mathematics (Sprlnger-Verlag) ; 1707. QA3.[_28 no. 1707 [QA402.3] 510 s - - d c 2 1 [629.8'312] 99-16712 CIP
Mathematics Subject Classification (1991): 49M 1O, 49J 15, 90C30, 65L06 ISSN 0075- 8434 ISBN 3-540-66214-6 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. 9 Springer-Verlag Berlin Heidelberg 1999 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10650221 41/3143-543210 - Printed on acid-free paper
Dedicated to Ela
Preface
The material presented in this book is the result of the author's work at the Interdisciplinary Centre for Process Systems Engineering at Imperial College, London. In initial stages, for the period of first nine months, the work was supported by the British Council, then directly by the Centre where the author was employed until August 1998. Originally, the aim of the work was to provide numerical methods for optimal control problems with state constraints. At that time, that is, in early 1990s, the methods available for these problems (with the exception of the work [42], which is discussed later) were either the methods based on full discretization (parametrization of state and control variables), or they were function space algorithms (where decision variables were measurable functions). The first group of methods assumed a p r i o r i discretization of system equations, and thus exc
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