Differential Inclusions Set-Valued Maps and Viability Theory
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Editors
M. Artin S. s. Chern J. M. Frohlich A. Grothendieck E. Heinz H. Hironaka F. Hirzebruch L. Hormander S. Mac Lane W. Magnus C. C. Moore J. K. Moser M. Nagata W. Schmidt D. S. Scott J. Tits B. L. van der Waerden M. Waldschmidt s. Watanabe Managing Editors
M. Berger B. Eckmann
s. R. S. Varadhan
Jean-Pierre Aubin Arrigo Cellina
Differential Inclusions Set-Valued Maps and Viability Theory
With 29 Figures
Springer-Verlag Berlin Heidelberg New York Tokyo 1984
Jean-Pierre Aubin CEREMADE, Universite de Paris-Dauphine Place du Marechal de Latte de Tassigny 75775 Paris Cedex 16 France Arrigo Cellina S.I.S.S.A. Strada Costiera 11 Trieste Italy
AMS Subject Classification (1980): 34A60, 34D, 39A,B, 49A,E
ISBN-13: 978-3-642-69514-8
001: 10.1007/978-3-642-69512-4
e-ISBN-13: 978-3-642-69512-4
Library of Congress Cataloging in Publication Data Aubin, Jean-Pierre. Differential inclusions. (Grundlehren der mathematischen Wissenschaften; #264) Bibliography: p. Includes index. 1. Differential inclusions, 2. Set-valued maps. 3. Feedback control systems. I. Cellina, Arrigo, 1941. II. Title. III. Title: Viability theory. IV. Series. QA371.A93 1984 515.3'5 84-1327 ISBN-13: 978-3-642-69514-8 (U.S.) This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© Springer-Verlag Berlin Heidelberg 1984 Softcoverreprint ofthe hardcover 1st edition 1984
2141/3140-543210
This book is dedicated to Anne-Laure, Claudia and Francesca
_ _ _. . . pigraph Why a book on differential inclusions?
There is a great variety of motivations that led mathematicians to study dynamical systems having velocities not uniquely determined by the state of the system, but depending loosely upon it, i.e., to replace differential equations x'= f(x)
by differential inclusions x'EF(x)
when F is the set-valued map that associates to the state x of the system the set of feasible velocities. Each one of these motivations offered a partial and biased view of differential inclusions, but all together contributed to the creation of a wealth of problems to a subject whose vitality is at present beyond doubts. The first purpose of this book is to report on the common tools and ideas which were devised and proposed by those who were attracted by this field either for its own intrinsic interest and beauty or for its potential for applications in different fields . But, besides this array of mathematical and physical motivations, social and biological sciences should provide many instances of differential inclusions. Indeed, if deterministic models are quite convenient for describing systems that arise in physics, mechanics, engineering and even, in microeconomics, their use for explaining th
