Viability Characterizations and Construction of Celerity Regulators
This chapter provides the mathematical characterization of averagers, Cournot, reachable and Eupalinian maps without using the evolutions governed by the differential inclusions involved in their definitions. Hence, the resolution of differential inclusio
- PDF / 4,568,932 Bytes
- 254 Pages / 453.543 x 683.15 pts Page_size
- 37 Downloads / 212 Views
Jean-Pierre Aubin Anya Désilles
Traffic Networks as Information Systems A Viability Approach
Mathematical Engineering Series editors Claus Hillermeier, Neubiberg, Germany Jörg Schröder, Essen, Germany Bernhard Weigand, Stuttgart, Germany
More information about this series at http://www.springer.com/series/8445
Jean-Pierre Aubin Anya Désilles •
Traffic Networks as Information Systems A Viability Approach
123
Anya Désilles VIMADES Paris France
Jean-Pierre Aubin VIMADES Paris France
ISSN 2192-4732 Mathematical Engineering ISBN 978-3-642-54770-6 DOI 10.1007/978-3-642-54771-3
ISSN 2192-4740
(electronic)
ISBN 978-3-642-54771-3
(eBook)
Library of Congress Control Number: 2016938376 © Springer-Verlag Berlin Heidelberg 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer-Verlag GmbH Berlin Heidelberg
We dedicate this book to our dei ex machina, Alexandre Bayen, Christian Claudel, Gaël Désilles and Patrick Saint-Pierre and to the next generation around Nathalie and Nicolas Désilles and Pierre-Cyril Aubin-Frankowski.
Preface
The purpose of this book is to study 1. Traffic networks as information systems advising velocities to vehicles at each time and position through celerity regulators we have to construct; 2. By using a viability approach. Although the abstract nature of the mathematical approach of this book is common to several types of networks, synaptic networks, biological networks, economic networks, etc., this book focuses mainly on road networks to anchor the main concepts, enunciate some traffic problems and solve them. Road networks are indeed familiar to everyone, whereas other applications require some knowledge of cognitive, biological, and financial sciences, economics, etc. For road systems, vehicles are driven by human brains that learned how to pilot the vehicles to link a departure position to an arrival one while staying on the road a
Data Loading...
