Stochastic Reachability Analysis of Hybrid Systems
Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybri
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Series Editors A. Isidori r J.H. van Schuppen r E.D. Sontag r M. Thoma r M. Krstic
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Luminita Manuela Bujorianu
Stochastic Reachability Analysis of Hybrid Systems
Luminita Manuela Bujorianu School of Mathematics University of Manchester Manchester UK
ISSN 0178-5354 e-ISSN 2197-7119 Communications and Control Engineering ISBN 978-1-4471-2794-9 e-ISBN 978-1-4471-2795-6 DOI 10.1007/978-1-4471-2795-6 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2012932743 Mathematics Subject Classification (2010): 60J27, 60J25, 60J35, 60J40, 60J60, 60K15, 62F15, 60G40, 32U20, 93C30, 34A38, 49J40, 49J55, 49L20, 49L25, 35J99, 47B34, 45H05 © Springer-Verlag London Limited 2012 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of 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 laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
In memory of Elena and Constanta
Preface
The concept of hybrid systems is a mathematical model for real life systems whose behaviour involves a mixture of discrete and continuous dynamics. Such systems are everywhere around us, from the simple bouncing ball to sophisticated cars, trains, planes and robots. Basically, every form of life exhibits a hybrid dynamics. Most physical and meteorological phenomena exhibit a hybrid dynamics. For scientists and engineers, the systems of interest are those for which the discrete and continuous dynamics interact or are connected. This interaction can take many forms, but the most common one occurs when discrete/digital controllers switch between different continuous processes. Other forms of interaction include discrete transitions that depend on continuous evolutions, or other appear as result of a decision process, or because of the occurrence of certain events. These systems are not given a distinct name. Most recently, the term cyber-physical systems has been proposed to denote collections of such interacting systems as networked or multi-agent hybri
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