Introduction to Discrete Event Systems is a comprehensive introduction to the field of discrete event systems, offering a breadth of coverage that makes the material accessible to readers of varied backgrounds. The book emphasizes a unified modeling framework that transcends specific application areas, linking the following topics in a coherent manner: language and automata theory, supervisory control, Petri net theory, Markov chains and queuing theory, discrete-event simulation, and concurrent estimation techniques. This edition includes recent research results pertaining to the diagnosis of discrete event systems, decentralized supervisory control, and interval-based timed automata and hybrid automata models.

Introduction to Discrete Event Systems

A discrete event system (DES) is a dynamic system that evolves in accordance with the abrupt occurrence, at possibly unknown irregular intervals, of physical events. Such systems arise in a variety of contexts ranging from computer operating systems to the control of complex multimode processes. A control theory for the logical aspects of such DESs is surveyed. The focus is on the qualitative aspects of control, but computation and the related issue of computational complexity are also considered. Automata and formal language models for DESs are surveyed. >

The control of discrete event systems

This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints. The linearity has to be understood with respect to nonstandard algebraic structures, e.g. the 'max-plus algebra'. A calculus is developed based on such structures, which is followed by tools for computing the time behaviour to such systems. This algebraic vision lays the foundation of a bona fide 'discrete event system theory', which is shown to parallel the classical linear system theory in several ways.

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Synchronization and Linearity: An Algebra for Discrete Event Systems

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Reversibility and Stochastic Networks

Max-algebra: Two Special Features.- One-sided Max-linear Systems and Max-algebraic Subspaces.- Eigenvalues and Eigenvectors.- Maxpolynomials. The Characteristic Maxpolynomial.- Linear Independence and Rank. The Simple Image Set.- Two-sided Max-linear Systems.- Reachability of Eigenspaces.- Generalized Eigenproblem.- Max-linear Programs.- Conclusions and Open Problems.

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Max-linear Systems: Theory and Algorithms

A discrete-event system is a system whose behavior can be described by means of a set of time-consuming activities, performed according to a prescribed ordering. Events correspond to starting or ending some activity. An analogy between linear systems and a class of discrete-event systems is developed. Following this analogy, such discrete-event systems can be viewed as linear, in the sense of an appropriate algebra. The periodical behavior of closed discrete-event systems, i.e., involving a set of repeatedly performed activities, can be totally characterized by solving an eigenvalue and eigenvector equation in this algebra. This problem is numerically solved by an efficient algorithm which basically consists of finding the shortest paths from one node to all other nodes in a graph. The potentiality of this approach for the performance evaluation of flexible manufacturing systems is emphasized; the case of a flowshop-like production process is analyzed in detail.

A linear-system-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing

It is shown that a certain class of Petri nets called event graphs can be represented as linear time-invariant finite-dimensional systems using some particular algebras. This sets the ground on which a theory of these systems can be developed in a manner which is very analogous to that of conventional linear system theory. Some preliminary basic developments in that direction are shown. Several ways in which one can consider event graphs as linear systems are described. These correspond to approaches in the time domain, in the event domain, and in a two-dimensional domain. In each of these approaches, a different algebra has to be used for models to remain linear, but the common feature of these algebras is that they all fall into the axiomatic definition of 'dioids'. A unified presentation of basic algebraic results on dioids is provided. >

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Algebraic tools for the performance evaluation of discrete event systems

A discrete-event system is a system whose behavior can be described by means of a set of time-consuming activities, performed according to a prescribed ordering. Events correspond to starting or ending some activity. An analogy between linear systems and a class of discrete-event systems is developed. Following this analogy, such discrete-event systems can be viewed as linear, in the sense of an appropriate algebra. The periodical behavior of closed discrete-event systems, i.e. involving a set of repeatedly performed activities, can be totally characterized by solving an eigenvalue and eigenvector equation in this algebra. This problem is numerically solved by an efficient algorithm which basically consists in finding the shortest paths from one node to all other nodes in a graph. The potentiality of this approach for the performance evaluation of repetitive production processes is illustrated on an example.

A linear-system-theoretic view of discrete-event processes

In this paper, we pursue the Analogy between classical linear System Theory and a new "linear" Theory for Discrete-Event Dynamic Systems which has been introduced for the first time in [3] and which is based on the algebra of "dioids". We first define the particular class of timed Petri nets that can be described by "linear" recurrent equations and then develop concepts such as transfer matrix representations of such systems, stability, observability, controllability, feed-back stabilization, realization of transfer matrices etc...

Linear system theory for discrete event systems

https://hal.inria.fr/inria-00076367/document

M. Viot

Papers

A linear-system-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing

Algebraic tools for the performance evaluation of discrete event systems

A linear-system-theoretic view of discrete-event processes

Linear system theory for discrete event systems

Analyse du comportement periodique de systemes de production par la theorie des dioides