Viability Theory.pdf

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Viability Theory

Acknowledgments

Contents

List of Figures

Chapter 1: Overview and Organization

Part I Viability Kernels and Examples

Part II Mathematical Properties of Viability Kernels

Part III First-Order Partial Differential Equations

Part IV Appendices

Viability Theory

•

Jean-Pierre Aubin • Alexandre M. Bayen Patrick Saint-Pierre Viability Theory New Directions Second Edition 123

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 bayen@berkeley.edu Prof. Jean-Pierre Aubin VIMADES 14 rue Domat 75005 Paris France aubin.jp@gmail.com Prof. Patrick Saint-Pierre Universit´e Paris Dauphine LEDA-SDFi 12 rue de la Roue 92140 Clamart France patrick.saint.pierre@gmail.com ISBN 978-3-642-16683-9 DOI 10.1007/978-3-642-16684-6 Springer Heidelberg Dordrecht London New York e-ISBN 978-3-642-16684-6 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)

`A Pierre-Cyril Aubin-Frankowska et `a sa maman, H´el`ene Frankowska, `A la m´emoire de Fran¸cois Bayen, `A Catherine, Fran¸cois, Claire, Jean-Benoˆıt, Guillaume Saint-Pierre et `a Odile Perrier-Saint-Pierre.

•

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- Gorre, Pierre Cardaliaguet, Luxi Chen, Christian Claudel, ´Eva Cr¨uck, Anya D´esilles, Ga¨el D´esilles, Olivier Dordan, Halim Doss, luc Doyen, Marie- H´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 beneﬁted from fruitful conversations with Carlos Daganzo, Miroslav Krstic, Michael Cassidy, Benedetto Piccoli, Christian Claudel, Sebastien Blandin and Xavier Litrico. The simulations using the software of the viability algorithms are due to Patrick Saint-Pierre and the ﬁgures to Alexandre Bayen and Patrick Saint- Pierre. The experiment on the pioneer has been made by ´Eva Cr¨uck, Ga¨el D´esilles, Benjamin Frenais de Coutard, Aur´elien Gosselin, Fabrice Leroux at D´el´egation G´en´erale `a l’Armement (DGA). The design and implementation of the viability algorithm used to compute the optimal trajectories of the submarine was done by Andrew Tinka. The submarine used for the experiments presented in this book was manufactured by the University of Porto, by the team of Joao Sousa, who is gratefully acknowledged for enabling ﬁeld experimental tests in the United States. The authors would like to thank Werner M¨uller for his 6-years patience as well as Catriona Byrne and Martina Bihn for their help for publishing this book. vii

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