The Theory and Application of Differential Games: Proceedings of the NATO Advanced Study Institute held at the University of Warwick, Coventry, England, 27 August–6 September, 1974 PDF
Preview The Theory and Application of Differential Games: Proceedings of the NATO Advanced Study Institute held at the University of Warwick, Coventry, England, 27 August–6 September, 1974
The Theory and Application of Differential Games NATO ADVANCED STUDY INSTITUTES SERIES Proceedings of the Advanced Study Institute Programme, which aims at the dissemination of advanced knowledge and the formation of contacts among scientists from different countries The series is published by an international board of publishers in conjunction with NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics London and New York C Mathematical and D. Reidel Publishing Company Physical Sciences Dordrecht and Boston D Behavioral and Sijthoff International Publishing Company Social Sciences Leiden E Applied Sciences Noordhoff International Publishing Leiden Series C - Mathematical and Physical Sciences Volume 13 - The Theory and Application of Differential Games The Theory and Application of Differential Games Proceedings of the NATO Advanced Study Institute held at the University of Warwick, Coventry, England, 27 August-6 September, 1974 edited by J. D. GROTE Control Theory Centre, University of Warwick, Coventry, England D. Reidel Publishing Company Dordrecht-Holland / Boston-U.S.A. Published in cooperation with NATO Scientific Affairs Division Library of Congress Cataloging in Publication Data Nato Advanced Study Institute, University of Warwick, 1974. The theory and application of differential games. (NATO advanced study institutes series: Series C, mathematical and physical sciences; v. 13) Includes bibliographies. 1. Differential games-Congresses. I. Grote, J. D., ed. II. Title. III. Series. QA269.N37 1974 519.3 74-34041 ISBN-13: 978-94-010-1806-7 e-ISBN-13: 978-94-010-1804-3 DOl: 10.1007/978-94-010-1804-3 Published by D. Reidel Publishing Company P.O. Box 17. Dordrecht. Holland Sold and distributed in the U.S.A .• Canada. and Mexico by D. Reidel Publishing Company, Inc. 306 Dartmouth Street. Boston, Mass. 02116, U.S.A. All Rights Reserved Copyright © 1975 by D. Reidel Publishing Company, Dordrecht Softcover reprint of the hardcover 1s t edition 1975 No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher CONTENTS PREFACE IX LIST OF PARTICIPANTS XI R. Isaacs THE PAST AND SOME BITS OF THE FUTURE L. D. Berkovi tz TWO PERSON ZERO SUM DIFFERENTIAL GAMES: AN OVERVIEW 13 R. J. Elliott INTRODUCTION TO DIFFERENTIAL GAMES I: COMPETITIVE DYNAMIC SITUATIONS, STRATEGIES, AND VALUES 23 R.J. Elliott INTRODUCTION TO DIFFERENTIAL GAMES II: STOCHASTIC GAMES AND PARABOLIC EQUATIONS 35 N.J. Kalton DIFFERENTIAL GAMES OF SURVIVAL 45 J.D. Grote SOLUTION SETS FOR N-PERSON GAMES 63 H.S. Witsenhausen ALTERNATIVES TO THE TREE MODEL FOR EXfENSIVE GAMES 77 G. Leitmann COOPERATIVE AND NON-COOPERATIVE DIFFERENTIAL GAMES 85 P. Varaiya N-PERSON STOCHASTIC DIFFERENTIAL GAMES 97 A. Blaquiere QUANTITATIVE GAMES: PROBLEM STATEMENT AND EXAMPLES, NEW GEOMETRIC ASPECTS 109 VI CONTENTS P. Levine STRATEGIC "PREJUDGMENTS" AND DECISION CRITERIA IN N-PERSON GAMES 121 W.E. Schmitendorf MANY PLAYER DIFFERENTIAL GAMES WITH COALITIONS 133 H. Moulin EXTENSION OF 2 PERSON ZERO SUM GAME 145 E.O. Roxin DIFFERENTIAL GAMES WITH PARTIAL DIFFERENTIAL EQUATIONS 157 L.D. Berkovitz THE TACTICAL AIR GAME: A MULTIMOVE GAME WITH MIXED STRATEGY SOLUTION 169 J. Case IMPULSIVELY CONTROLLED D.G. 179 K. Shell THE THEORY OF HAMILTONIAN DYNAMICAL SYSTEMS, AND AN APPLICATI.ON TO ECONOMICS 189 R.J. Elliott AVERAGED HAMILTONIANS IN DIFFERENTIAL GAMES 201 LoF. Pau COMPUTATIONAL ASPECTS IN TWO-LEVEL DIFFERENTIAL GAMES 209 D. Tabak COMPUTED SOLUTIONS OF DIFFERENTIAL GAMES 221 J. Bradley and P.L. Yu OPTIMALITY AND TRANSITION SURFACES USING THE REPRISAL CONCEPT 229 J. V. Breakwell PURSUIT OF A FASTER EVADER 243 H.J. Kelley and L. Lefton AERIAL TURNING CHASES 257 T.L. Vincent AVOIDANCE OF GUIDED PROJECTILES 267 CONTENTS VII o. Hajek PURSUIT GAMES: A SURVEY 281 N.J. Kalton VALUES OF POSITIONAL GAMES 293 L. Markus CATASTROPHE THEORY IN DIFFERENTIABLE GAMES 301 PREFACE The ~irst international con~erence on differential games was held at Amherst, Massachusetts, in September 1969. A second meeting, partially supported by N.A.T.O., was held in Varenna, Italy, in June 1970. At these conferences many new theoretical results and applications, especially in economic problems, were presented. The present volume consists o~ the lectures presented at a N.A.T.O. Advanced Study Institute on the "Theory and Applications of Differential Games" held at the University of Warwick, Coventry, England, from 27th August to 6th September, 1974. The main contributions during the first week consisted of a survey of two person zero sum differential games by L. D. Berkovitz and four integrated lectures by R. J. Elliott and N. J. Kalton, who have made important contributions to the concept of "value" of a differential game. Applications were featured during the second week and included tactical air games, pursuit and evasion problems, as well as computational aspects. A closing lecture with historical perspectives was given by Rufus Issacs, the recognised pioneer of differential games theory. The time-table received much favourable comment and may be worth recording here as close to the optimum - there were no more than 4 lectures a day at 9.30, 11.30, 14.30 and 16.00, wi th a long break at 10. 30 and a two hour lunch break. This left very ample time for formal discussions to run on if necessary, and also for much informal discussion outside the lecture theatre. Preprints were available for all participants on arrival. Evening social events were organised every other day and two weekend excursions were also arranged. The lectures are presented here in the order of presentation, except for the Elliott-Kalton lectures which have x PREFACE been placed together. It is hoped that the present volume will provide an up-to-date picture of this active field of research, presented however in tutorial fashion and suitable for those who are beginners. Much work goes into organising a meeting such as this one and I should like to thank particularly Dr. J. D. Grote who has acted as Editor of this volume and Mrs. Joan Carrington and Mrs. Caroline Howard-Williams who helped with the large volume of correspondence and other paper work that such a meeting generates. Patrick C. Parks Director of the NATO Advanced Study Institute on Differential Games, 27th August - 6th September 1974 Control Theory Centre, University of Warwick, Coventry, cv4 7AL, England. 14th November, 1974. LIST OF PARTICIPANTS Abramatic, J.-F. C. Centre d'Automatique, 35 Rue St. Honore, 77305, Fontainbleau, France. Allwright, J.C. Department of Computing & Control, Electrical Engineering Building, Imperial College, London, S.W.7., England. Baranger, J.R. SANTI, Universit~ de Lyon 1, 43 Boulevard 11 novembre 191e, 69 Villeurbane, France. Basar, T. Applied Mathematics Division, Marmara Research Institute, P.K. 141, Kadik8y, Istanbul, Turkey. Battinelli, A. Laboratorio Per Recerche di Dinamica dei Bistemi e di Elettronica Biomedica del C.N.R., Galleria Trieste 6, 35100 Padova, Italy. Becker, H.E. Universit~t Trier-Kaiserslautern, 675 Kais erslautern , Pfaffenbergstrasse 95, W. Germany. Berkovitz, L.D. Department of Mathematics, Purdue University, West Lafayette, Indiana 47906, U.S.A. Blaqui~re, A. Laboratoire d'Automatique Theorique, Universit~ de Paris 7, Tour 14-24 Se 'etage, 2 Place Jussieu, Paris 5, France. Breakwell, J.V. A/A Department, Durand 113, Stanford University, Stanford, California 94305, U.S.A. Case, J. Mathematical Sciences Department, John Hopkins University, Balitmore, Maryland 21218, U.S.A.
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