Book contents
- Frontmatter
- Contents
- Foreword
- Preface
- List of Participants
- An introduction to idempotency
- Tropical semirings
- Some automata-theoretic aspects of min-max-plus semirings
- The finite power property for rational sets of a free group
- The topological approach to the limitedness problem on distance automata
- Types and dynamics in partially additive categories
- Task resource models and (max, +) automata
- Algebraic system analysis of timed Petri nets
- Ergodic theorems for stochastic operators and discrete event networks.
- Computational issues in recursive stochastic systems
- Periodic points of nonexpansive maps
- A system-theoretic approach for discrete-event control of manufacturing systems
- Idempotent structures in the supervisory control of discrete event systems
- Maxpolynomials and discrete-event dynamic systems
- The Stochastic HJB equation and WKB method
- The Lagrange problem from the point of view of idempotent analysis
- A new differential equation for the dynamics of the Pareto sets
- Duality between probability and optimization
- Maslov optimization theory: topological aspect
- Random particle methods in (max, +) optimization problems
- The geometry of finite dimensional pseudomodules
- A general linear max-plus solution technique
- Axiomatics of thermodynamics and idempotent analysis
- The correspondence principle for idempotent calculus and some computer applications
Idempotent structures in the supervisory control of discrete event systems
Published online by Cambridge University Press: 05 May 2010
- Frontmatter
- Contents
- Foreword
- Preface
- List of Participants
- An introduction to idempotency
- Tropical semirings
- Some automata-theoretic aspects of min-max-plus semirings
- The finite power property for rational sets of a free group
- The topological approach to the limitedness problem on distance automata
- Types and dynamics in partially additive categories
- Task resource models and (max, +) automata
- Algebraic system analysis of timed Petri nets
- Ergodic theorems for stochastic operators and discrete event networks.
- Computational issues in recursive stochastic systems
- Periodic points of nonexpansive maps
- A system-theoretic approach for discrete-event control of manufacturing systems
- Idempotent structures in the supervisory control of discrete event systems
- Maxpolynomials and discrete-event dynamic systems
- The Stochastic HJB equation and WKB method
- The Lagrange problem from the point of view of idempotent analysis
- A new differential equation for the dynamics of the Pareto sets
- Duality between probability and optimization
- Maslov optimization theory: topological aspect
- Random particle methods in (max, +) optimization problems
- The geometry of finite dimensional pseudomodules
- A general linear max-plus solution technique
- Axiomatics of thermodynamics and idempotent analysis
- The correspondence principle for idempotent calculus and some computer applications
Summary
Introduction
Discrete event systems (DES) are characterized by a collection of events, such as the completion of a job in a manufacturing process or the arrival of a message in a communication network. The system state changes only at time instants corresponding to the occurrence of one of the defined events. At the logical level of abstraction, the behavior of a DES is described by the sequences of events that it performs. However, if time constraints are of explicit concern in the system dynamics and its performance specification, its behavior can be characterized by sequences of occurrence times for each event. The objective of this paper is to demonstrate how underlying algebraic similarities between certain logical and timed DES can be exploited to study the control of timed DES.
Logical DES are often modelled by automata known as finite state machines (FSM). A FSM consists of a set of states Q, a collection of events Σ, and a state transition function δ. The occurrence of an event causes the system to move from one state to another as defined by the transition function.
Timed DES which are subject to synchronization constraints can be modelled by automata known as timed event graphs (TEG). A TEG is a timed place Petri net in which forks and joins are permitted only at transitions. A delay or processing time is associated with each place connecting pairs of transitions. Each transition in the graph corresponds to an event in the system. When an event occurs it initiates the processes connecting it to successor events.
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- Idempotency , pp. 262 - 281Publisher: Cambridge University PressPrint publication year: 1998