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
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`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.
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