Ratnesh Kumar and Vijay K. Garg
ISBN 0-7923-9538-7
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Modeling and Control of Logical Discrete Event Systems
Ratnesh Kumar and Vijay K. Garg ISBN 0-7923-9538-7
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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.
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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
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