Viability Theory New Directions
Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from b
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Jean-Pierre Aubin • Alexandre M. Bayen Patrick Saint-Pierre
Viability Theory New Directions Second Edition
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Prof. Jean-Pierre Aubin VIMADES 14 rue Domat 75005 Paris France [email protected] Prof. Patrick Saint-Pierre Universit´e Paris Dauphine LEDA-SDFi 12 rue de la Roue 92140 Clamart France [email protected]
Prof. Dr.-Ing. Alexandre M. Bayen University of California at Berkeley Electrical Engineering and Computer Sciences Civil and Environmental Engineering Sutardja Dai Hall 642 Berkeley CA 94720 USA [email protected]
ISBN 978-3-642-16683-9 e-ISBN 978-3-642-16684-6 DOI 10.1007/978-3-642-16684-6 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011932723 First edition was published with Birkh¨auser Boston. c Springer-Verlag Berlin Heidelberg 2011 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm 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. Violations are liable to prosecution under the German Copyright Law. 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. Cover design: eStudio Calamar, Berlin/Figueres Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
` Pierre-Cyril Aubin-Frankowska et a` sa A maman, H´el`ene Frankowska, ` la m´emoire de Fran¸cois Bayen, A ` Catherine, Fran¸cois, Claire, A Jean-Benoˆıt, Guillaume Saint-Pierre et a` Odile Perrier-Saint-Pierre.
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Acknowledgments
The authors would like to thank H´el`ene Frankowska for her implicit and explicit contributions to the writing of the book, as well as the members of the “viability group” who participated to its elaboration: Anne Bru´ Cr¨ Gorre, Pierre Cardaliaguet, Luxi Chen, Christian Claudel, Eva uck, Anya D´esilles, Ga¨el D´esilles, Olivier Dordan, Halim Doss, luc Doyen, MarieH´el`ene Durand, Alexandra Fronville, Thomas Lorenz, Sophie Martin, Juliette Mattioli, Frank Maurin, Alberto Murillo, Laurent Najman, Dominique Pujal, Marc Quincampoix and Nicolas Seube without forgetting Alain Haurie, Mich`ele Breton and Georges Zaccour. We also would like to thank Andr´e Giroux for his careful reading of the first part of this book. The authors want to thank Claire Tomlin, Ian Mitchell, Meeko Oishi, Shankar Sastry, George Pappas, John Lygeros and Craig Evans for fruitful discussions leading to the initial formulation of the landing problem and reachability analysis. The chapter on the traffic and conservations laws greatly b
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