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Modeling and Control of Logical Discrete Event Systems

Ratnesh Kumar and Vijay K. Garg

ISBN 0-7923-9538-7

·  About the book

·  Table of contents

·  Known errors in the book

About the book

The field of discrete event systems has emerged to provide a formal treatment of many of the man-made systems such as manufacturing systems, communication networks, automated traffic systems, database management systems, and computer systems that are event-driven, highly complex, and not amenable to the classical treatments based on differential or difference equations. Discrete event systems is a growing field that utilizes many interesting mathematical models and techniques. In this book we focus on a high level treatment of discrete event systems, where the order of events, rather than their occurrence times, is the principal concern. Such treatment is needed to guarantee that the system under study meets desired logical goals. In this framework, discrete event systems are modeled by formal languages or, equivalently, by state machines. The field of logical discrete event systems is an interdisciplinary field---it includes ideas from computer science, control theory, and operations research. Our goal is to bring together in one book the relevant techniques from these fields. Modeling and Control of Logical Discrete Event Systems is the first book of this kind for the professionals in the area of discrete event systems. The book is also designed for a graduate level course on logical discrete event systems. It contains all the necessary background material in formal language theory and lattice theory. The only prerequisite is some degree of ``mathematical maturity''. Several examples and exercise problems are included in each chapter to facilitate classroom teaching.

Table of contents

PREFACE 1 Introduction to Formal Language Theory 1.1 Introduction 1.2 Languages 1.3 State Machines 1.4 Regular Languages 1.5 Non-Regular Languages 1.6 Exercises 1.7 Bibliographic Remarks 2 Introduction to Lattice Theory 2.1 Partial Order and Lattice 2.2 Extremal Fixed Points 2.3 Dual, Co-Dual, Inverse, and Converse Operations 2.4 Extremal Solutions of Inequations 2.5 Remark on Inverse Operation 2.6 Exercises 2.7 Bibliographic Remarks 3 Control under Complete Observation 3.1 Introduction 3.2 Centralized Control 3.3 Modular Control 3.4 Exercises 3.5 Bibliographic Remarks 4 Control under Partial Observation 4.1 Introduction 4.2 Centralized Control 4.3 Modular Control 4.4 Decentralized Control 4.5 Exercises 4.6 Bibliographic Remarks 5 Control of Non-terminating Behavior 5.1 Introduction 5.2 Buchi Machine as Acceptor for w-languages 5.3 w-Controllability 5.4 Exercises 5.5 Bibliographic Remarks REFERENCES INDEX

Known errors in the book

  1. Theorem 5.6 and results that depend on this theorem (Corollary 5.2 and the algorithm of section 5.3.3) only hold under the additional restriction that B is w-closed. For the correct results when B is w-closed, see:

R. Kumar, V. K. Garg, S. I. Marcus, ``On w-Controllability and w-Observability of Discrete Event Dynamic Systems,'' IEEE Transactions on Automatic Control, Vol. 37, No. 12, December 1992, pp. 1978-1985.

For the more general case, supCw(B) can be expressed as the limit of a finite string language as shown in in Proposition 5.2 (a) of

Thistle, J. G. and W. M. Wonham, "Supervision of Infinite Behaviour of Discrete-Event Systems", SIAM J. Control and Optimization, Vol. 32, No. 4, July 1994, pp. 1098 -- 1113.

For the computation of supCw(B), see:

Thistle, J. G., "On Control of Systems Modelled as Deterministic Rabin Automata", Discrete Event Dynamic Systems: Theory and Applications", Vol. 5, No. 4, Sept. 1995, pp. 357 -- 381.

  1. Algorithm for construction of K^M given on page 102 is incorrect. A correct algorithm appears in 1995 CDC paper of Kumar-Shayman.

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