Supervision of Petri Nets
Supervision of Petri Nets presents supervisory control theory for Petri nets with a legal set as the control goal. Petri nets model discrete event systems - dynamic systems whose evolution is completely determined by the occurrence of discrete events. Con
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THE KLUWER INTERNATIONAL SERIES ON DISCRETE EVENT DYNAMIC SYSTEMS Series Editor
Yu-ChiHo Harvard University ANALYSIS OF MANUFACTURING ENTERPRISES: An Approach to Leveraging Value Delivery Processes for Competitive Advantage N. Viswanadham ISBN: 0-7923-8671 -X INTRODUCTION TO DISCRETE EVENT SYSTEMS Christos G. Cassandras, Stephane Lafortune ISBN: 0-7923-8609-4 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 SUPERVISORY CONTROL OF DISCRETE EVENT SYSTEMS USING PETRI NETS John O. Moody and Panos J. Antsaklis ISBN: 0-7923-8199-8 GRADIENT ESTIMATION VIA PERTURBATION ANALYSIS P. G1asserman 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 lian-Qiang HU
SUPERVISION OF PETRI NETS
by
Geert Stremersch University of Ghent, Belgium
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library ofCongress Cataloging-in-Publication Data Strernersch, G. (Geert), 1973Supervision of Petri nets I Geert Strernersch. p. crn. - (The Kluwer international series on discrete event dynamic systerns) Includes bibliographical references and index. ISBN 978-1-4613-5603-5 ISBN 978-1-4615-1537-1 (eBook) DOI 10.1007/978-1-4615-1537-1 l. Petri nets. 2. Control theory. 1. Title. II. Series QA267.S7652001 511.3 --dc21
2001046195
Copyright © 2001 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2001 Softcover reprint ofthe hard.cover Ist ed.ition 2001 AII rights reserved. No part ofthis publication rnay be reproduced, stored in a retrieval systern or transmitted in any form or by any rneans, rnechanical, photo-copying, recording, or otherwise, without the prior written permission ofthe publisher, Springer Science+Business Media, LLC. Printed on acid-free paper.
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Contents
Preface
xi
1. THE PETRI NET MODEL 1 Discrete event systems 2 Notation 3 Order theoretical preliminaries 3.1 Partially ordered sets 3.2 Lattices 3.3 Up- and down-sets 4 Petri net definition 5 Petri nets as discrete event system models 6 Reachable sets 7 Graphical representation 8 Reachability via subsets of transitions 9 Other concurrency assumptions 9.1 The no concurrency assumption 9.2 The concurrency assumption 10 A general Petri net definition 11 Notes and references
1 1 4 5 6 6 7 8 10 12 14 18 20 21 23 24 26
2. SUPERVISORY CONTROL 1 Control goal and architecture 2 Formal definition 3 Reachable sets under supervision 4 Maxima
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