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随机混合系统 -Christos G. Cassandras
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随机混合系统 -由Christos G. Cassandras所·写
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CRC is an imprint of the Taylor & Francis Group,
an informa business
Boca Raton London New York
Stochastic
Hybrid Systems
edited by
Christos G. Cassandras
Boston University
John Lygeros
ETH Zürich, Switzerland
9083_C000.indd 1 10/09/2006 11:20:19 AM
© 2007 by Taylor & Francis Group, LLC
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CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487‑2742
© 2007 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed in the United States of America on acid‑free paper
10 9 8 7 6 5 4 3 2 1
International Standard Book Number‑10: 0‑8493‑9083‑4 (Hardcover)
International Standard Book Number‑13: 978‑0‑8493‑9083‑8 (Hardcover)
This book contains information obtained from authentic and highly regarded sources. Reprinted
material is quoted with permission, and sources are indicated. A wide variety of references are
listed. Reasonable efforts have been made to publish reliable data and information, but the author
and the publisher cannot assume responsibility for the validity of all materials or for the conse‑
quences of their use.
No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any
electronic, mechanical, or other means, now known or hereafter invented, including photocopying,
microfilming, and recording, or in any information storage or retrieval system, without written
permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.
copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC)
222 Rosewood Drive, Danvers, MA 01923, 978‑750‑8400. CCC is a not‑for‑profit organization that
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photocopy license by the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and
are used only for identification and explanation without intent to infringe.
Library of Congress Cataloging‑in‑Publication Data
Cassandras, Christos G.
Stochastic hybrid systems / Christos G. Cassandras and John Lygeros.
p. cm.
Includes bibliographical references and index.
ISBN‑13: 978‑0‑8493‑9083‑8 (alk. paper)
ISBN‑10: 0‑8493‑9083‑4 (alk. paper)
1. Stochastic systems. 2. Control theory. I. Lygeros, John. II. Title.
QA274.2.C37 2007
003’.76‑‑dc22 2006025156
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
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9083_C000.indd 4 10/09/2006 11:20:20 AM
© 2007 by Taylor & Francis Group, LLC
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Preface
This book gives a tempting glimpse at what is arguably the most ambitious type of
dynamic systems that have been studied to date: stochastic hybrid systems. Stochas-
tic hybrid systems combine time-driven and event-driven dynamics and incorporate
the ubiquitous uncertainty elements within which a system must operate.
Problems in mathematical finance such as pricing of options and insurance were
among the first and very successful areas of application of stochastic hybrid meth-
ods. More recently, however, the great importance of stochastic hybrid systems in
engineering has also been widely recognized. Stochastic hybrid systems are among
the most common technological creations of modern society: every time a physi-
cal process interacts with computerized equipment in an uncertain environment, a
stochastic hybrid system is present. In modern automobiles, the physical processes
involved in the engine, brakes, or functions such as climate control and remote access
are subject to computerized controllers responsible for overall proper coordination
and response to unexpected occurrences. The same can be said of everyday devices
such as photocopiers, printers, and even computers themselves. Communication net-
works, manufacturing systems, and air traffic management are other examples of
technological environments where the same combination of physical (time-driven)
processes coordinated by computerized (event-driven) equipment in the presence of
uncertainty arises. More recently, many biological processes have also been cast
into the stochastic hybrid setting, opening up an exciting new way of viewing these
processes and, potentially, controlling them.
Following the usual scientific path in the study of dynamic systems, the book be-
gins with models for stochastic hybrid systems. Based on these models, one can
then develop specific analysis and synthesis techniques. In layman’s terms, one can
describe in plain English how a system ought to behave in order to meet some spec-
ifications. For example, a manufacturing process should produce x items of a given
type, each meeting a quality criterion y and each being delivered within t minutes
from being ordered with probability q. To implement this design specification, one
needs to develop a precise model of the manufacturing process as a stochastic hy-
brid system, to incorporate discrete events such as the completion of an item, time-
driven dynamics, and the uncertainty inherent in the manufacturing process. One
then needs to apply a particular set of design techniques geared toward stochastic
hybrid systems, to synthesize controllers achieving the desired goals.
The material contained in the first part of the book provides the underlying princi-
ples behind this process and a rigorous understanding of the basic design limitations
within which one must operate. Building on this fundamental exposition, the second
© 2007 by Taylor & Francis Group, LLC
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part of the book presents methods for implementing on a computer the calculations
necessary for applying stochastic hybrid systems analysis and synthesis techniques
in practice. Finally, the book casts examples of systems encountered in a wide range
of application areas into the stochastic hybrid systems framework and explains how
one can resolve practical problems associated with these systems.
The universal nature of stochastic hybrid systems makes the target audience of
this book unusually broad. The use of stochastic hybrid systems has gained partic-
ular appeal for designers and managers of communication networks and automated
manufacturing systems. It has also been associated with air traffic management and,
very recently, an interest in better understanding biological processes. However,
given the systems and control flavor of the material, the target audience is more
likely to be concentrated among academic researchers and R&D personnel in indus-
try with a background and interest in systems and control engineering and, to a lesser
extent, computer science. Specific examples include those working in settings that
rely on emerging embedded system technologies including automotive engineering,
aerospace, digital signal processing, and automated manufacturing.
Acknowledgments. The editors of this volume are grateful to all the contributing
authors for their exciting and timely contributions. They would also like to thank
Badis Djeridane for his comments on early drafts, Nora Konopka and Helena Red-
shaw of Taylor & Francis for their editorial guidance, and the CRC LaTex help desk
for their prompt assistance with the numerous formatting problems encountered dur-
ing the production of the volume. The editorial work was supported by the European
Commission, under the project HYGEIA, FP6-NEST-04995, by the U.S. National
Science Foundation under grant DMI-0330171, and by the U.S. Air Force Office of
Scientific Research under grants FA9550-04-1-0133 and FA9550-04-1-0208.
Christos G. Cassandras
Boston
John Lygeros
Z¨urich
September 19, 2006
© 2007 by Taylor & Francis Group, LLC
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About the Editors
Christos G. Cassandras is Professor of Manufacturing Engineering and Professor
of Electrical and Computer Engineering at Boston University. He is also co-founder
of Boston University’s Center for Information and Systems Engineering (CISE). He
received degrees from Yale University (B.S., 1977), Stanford University (M.S.E.E.,
1978), and Harvard University (S.M., 1979; Ph.D., 1982). In 1982–1984 he was
with ITP Boston, Inc. where he worked on the design of automated manufacturing
systems. In 1984–1996 he was a faculty member at the Department of Electrical
and Computer Engineering, University of Massachusetts/Amherst. He specializes
in the areas of discrete event and hybrid systems, stochastic optimization, and com-
puter simulation, with applications to computer and sensor networks, manufacturing
systems, and transportation systems. He has published over 200 refereed papers in
these areas, and two textbooks. He has guest-edited several technical journal issues
and serves on several journal editorial boards. Dr. Cassandras is currently Editor-in-
ChiefoftheIEEE Transactions on Automatic Control and has served as Editor for
Technical Notes and Correspondence and Associate Editor. He is a member of the
IEEE CSS Board of Governors, chaired the CSS Technical Committee on Control
Theory, and served as Chair of several conferences. He has been a plenary speaker
at various international conferences, including the American Control Conference in
2001 and the IEEE Conference on Decision and Control in 2002. He is the recipient
of several awards, including the Distinguished Member Award of the IEEE Control
Systems Society (2006), the 1999 Harold Chestnut Prize (IFAC Best Control Engi-
neering Textbook) for Discrete Event Systems: Modeling and Performance Analysis,
and a 1991 Lilly Fellowship. He is a member of Phi Beta Kappa and Tau Beta Pi.
He is also a Fellow of the IEEE.
John Lygeros completed a B.Eng. degree in electrical engineering in 1990 and an
M.Sc. degree in control in 1991, both at Imperial College of Science Technology
and Medicine, London. He obtained a Ph.D. in 1996 from the Electrical Engineering
and Computer Sciences Department, University of California, Berkeley. In 1996–
2000 he held a series of postdoctoral research appointments at the National Auto-
mated Highway Systems Consortium, M.I.T., and U.C. Berkeley. In parallel, he also
worked as a part-time research engineer at SRI International, Menlo Park, Califor-
nia, and as a Visiting Professor at the Mathematics Department of the Universit´ede
Bretagne Occidentale, Brest, France. Between July 2000 and March 2003 he was
a University Lecturer at the Department of Engineering, University of Cambridge,
Cambridge, U.K., and a Fellow of Churchill College, Cambridge. Between March
2003 and July 2006 he was an Assistant Professor at the Department of Electrical
© 2007 by Taylor & Francis Group, LLC
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