Modeling and Control of Logical Discrete Event
Systems Ratnesh
Kumar and Vijay K. Garg
ISBN 0792395387 

The
field of discrete event systems has emerged to provide a formal treatment of
many of the manmade systems such as manufacturing systems, communication
networks, automated traffic systems, database management systems, and
computer systems that are eventdriven, 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 fieldit 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. 
PREFACE
1 Introduction to Formal Language Theory 1.1 Introduction 1.2 Languages 1.3
State Machines 1.4 Regular Languages 1.5 NonRegular 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,
CoDual, 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 Nonterminating
Behavior 5.1 Introduction 5.2 Buchi Machine as
Acceptor for wlanguages 5.3 wControllability 5.4 Exercises
5.5 Bibliographic Remarks REFERENCES INDEX 
R.
Kumar, V. K. Garg, S. I. Marcus, ``On
wControllability and wObservability of Discrete Event Dynamic Systems,''
IEEE Transactions on Automatic Control, Vol. 37, No. 12, December 1992, pp.
19781985. 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 DiscreteEvent 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.

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