Introduction to Discrete Event Systems
A substantial portion of this book is a revised version of Discrete Event Systems: Modeling and Performance Analysis (1993), which was written by the first author and received the 1999 Harold Chestnut Prize, awarded by the International Federation of Auto
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THE KLUWER INTERNATIONAL SERIES ON DISCRETE EVENT DYNAMIC SYSTEMS Series Editor Yu·Chi 80 Harvard University OBJECT-ORIENTED COMPUTER SIMULATION OF DISCRETE-EVENT SYSTEMS Jerzy Tyszer ISBN: 0-7923-8506-3 TIMED PETRI NETS: Theory and Application Jiacun Wang ISBN: 0-7923-8270-6 GRADIENT ESTIMATION VIA PERTURBATION ANALYSIS P. Glasserman ISBN: 0-7923-9095-4 PERTURBATION ANALYSIS OF DISCRETE EVENT DYNAMIC SYSTEMS Yu-Chi Ho and Xi-Ren Cao ISBN: 0-7923-9174-8 PETRI NET SYNTHESIS FOR DISCRETE EVENT CONTROL OF MANUFACTURING SYSTEMS MengChu Zhou and Frank DiCesare ISBN: 0-7923-9289-2 MODELING AND CONTROL OF LOGICAL DISCRETE EVENT SYSTEMS Ratnesh Kumar and Vijay K. Garg ISBN: 0-7923-9538-7 UNIFORM RANDOM NUMBERS: THEORY AND PRACTICE Shu Tezuka ISBN: 0-7923-9572-7 OPTIMIZATION OF STOCHASTIC MODELS: THE INTERFACE BETWEEN SIMULATION AND OPTIMIZATION Georg Ch. Pflug ISBN: 0-7923-9780-0 CONDITIONAL MONTE CARLO: GRADIENT ESTIMATION AND OPTIMIZATION APPLICATIONS Michael FU and Jian-Qiang HU ISBN: 0-7923-9873-4 SUPERVISORY CONTROL OF DISCRETE EVENT SYSTEMS USING PETRI NETS John O. Moody and Panos J. Antsaklis ISBN: 0-7923-8199-8
INTRODUCTION TO
DISCRETE EVENT SYSTEMS
by
Christos G. Cassandras Boston University Stephane Lafortune The University of Michigan
~ Springer
Library of Congress Cataloging-in-Publication Data Cassandras, Christos G. Introduction to discrete event systems / by Cbristos G. Cassandras, Stepbane Lafortune. p. cm. Includes bibliograpbical references. Printed on acid-free paper ISBN 978-1-4757-4072-1 ISBN 978-1-4757-4070-7 (eBook) DOI 10.1007/978-1-4757-4070-7 1. System analysis. II. Title T57.6.C39 1999 003-dc21
@.
Discrete-time systems. 1. Lafortune. Stepbane, 1958- . 99-40716
© 1999 Sprioger Science+Business Media New Yorlt Originally published by Springe1:-Vetbg New YorIl
which results in achieving the desired state value at t = 1 (see Fig. 1.16) when (1.38) is solved. Intuitively, we can also see that Ul (t) has the property of achieving the desired behavior in minimum time, since it makes use of the maximum allowable control subject to lu(t)1 ~ 1. However, it is certainly not the only possible control law we can come up with. For example, U2(t)
={
1/2 for t ~ 2 0 for t > 2
also achieves our objective.
1.2.8
The Concept of Feedback
The idea of feedback is intuitively simple: Use any available information about the system behavior in order to continuously adjust the control input. Feedback is used in our everyday life in a multitude of forms. In a conversation, we speak when the other party is silent, and switch to listening when the other party is beginning to talk. In driving, we monitor the car's position and speed in order to continuously make adjustments through our control of the steering wheel and accelerator and brake pedals. In heating a house, we use a thermostat which senses the actual temperature in order to turn a furnace on or off.
26
I
Chapter 1 Systems and Models x(t)
1.
2.
Figure 1.16: Sample paths corresponding to controls
"1 (t), U2(t) in Example 1.10.
Returning to
