Optimization Methods and Applications
This edited book is dedicated to Professor N. U. Ahmed, a leading scholar and a renowned researcher in optimal control and optimization on the occasion of his retirement from the Department of Electrical Engineering at University of Ottawa in 1999. The co
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Applied Optimization Volume 52
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.
Optimization Methods and Applications Edited by
Xiaoqi Yang and Kok Lay Teo Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
and
Lou Caccetta School of Math ematics and Statistics. Curtin University of Technology, Australia
Springer-Science+Business Media, B.V
A c.r.P. Catalogue record for this book is available from the Library of Congre ss.
ISBN 978-1-4419-4850-2 ISBN 978-1-4757-3333-4 (eBook) DOI 10.1007/978-1-4757-3333-4
Printed on acid-free paper
All Rights Reserved © 2001 Springer Science +Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2001. Softcover reprint of the hardcover I st edition 200 I No part of the 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
Dr. Nasir U. AHMED
Contents
Preface
XI
An Appreciation of Professor N.U. Ahmed
xii i
A Publication List of Professor N.U. Ahmed
xvii
Part I
OPTIMAL CONTROL
1 PRACTICAL STABILITY OF IMPULSIVE DELAY DIFFERENTIAL EQUATIONS AND APPLICATIONS TO CONTROL PROBLEMS
3
Georq« Bull itujer tuul X inzlu Lin
1 2 3 4
Introduction Prelimina ries Main Results Application
References
4 4 6 10 21
2 A REVIEW OF ILL-CONDITIONING AND REGULARIZATION IN OPTIMAL CONTROL COMPUTATION Francis Betnjoh. asul Les S. .Ienninq« 1 Introduction 2 Optimal Control Problem Template for MISER3 3 Control Parametrization to except possibly at times t = Tk; and satisfies (2.1b) at each t = Tk for t > to. Definition 2.1 System (2.1) is said to be
6
OPTIMIZATION METHODS AND APPLICATIONS
(P 1) practically stable with respect to (A, a) where 0 < A :::; a if there exis ts some to E ~+ such that for all ¢ E PC r with II¢II r :::; A we have Ilx( t) II :::; a for all t ~ to where x (t ) = x(t ,to , ¢ ,T/) is any solution of (2. 1); (P 2) un iformly practically stable with respect to (A, a) if (Pt ) holds for all to E ~+ ; (P3 ) practically quasi stable with respect to (A, {3, T) where A, {3, T > 0 if there 1¢lIr :::; A we have exis ts some to E ~+ such that for all ¢ E PC r with 1 Ilx(t)11 :::; {3 for all t ~ to + T ; (P4) un iformly practically quasi stable with respect to (A,{3,T) if (P 3) holds for all to E ~+ ; (P5) stro ngly practically stable with respect to (A, a , {3, T) where 0 < {3 < A :::; a if th ere exists some to E ~+ such that for all ¢ E PC r with 11¢llr :::; A we have Ilx(t)11 :::; a for all t ~ to and Ilx(t)11:::; {3 for all t ~ to + T ; (P 6) un iformly strongly practically stable with respect to (A, a, {3, T) if (P 5) holds for all to E ~+. Giv en a functi on V E C([to - r , 00) X ~n , ~+) we define the genera lized derivative of V alon g a particular solution
