Philippe Declerck

Discrete Event Systems in Dioid Algebra and Conventional Algebra (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task - a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers. The content focuses on the modeling of a class of dynamic systems usually called "discrete event systems" where the timing of the events is crucial. Events are viewed as sudden changes in a process which is, essentially, a man-made system, such as automated manufacturing lines or transportation systems. Its main advantage is its formalism which allows us to clearly describe complex notions and the possibilities to transpose theoretical results between dioids and practical applications.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 164
• Erscheinungstermin: 13. Februar 2013
• Englisch
• ISBN-13: 9781118578629
• Artikelnr.: 38245041

Autorenporträt

Philippe Declerck is Senior Lecturer LISA / ISTIA Laboratory at University of Angers, France.

Inhaltsangabe

Chapter 1 Introduction

General introduction

History and three mainstays

Scientific context

Dioids

Petri nets

Time and algebraic models

Organization of the book

Chapter 2 Consistency

Introduction

Models

Physical point of view

Objectives

Preliminaries

Models and principle of the approach

P-time event graphs

Dater form

Principle of the approach (example)

Analysis in the "static" case

"Dynamic" model

Extremal acceptable trajectories by series of matrices

Lowest state trajectory

Greatest state trajectory

Consistency

Maximal horizon of temporal consistency

Date of the first token deaths

Computational complexity

Conclusion

Chapter 3 Cycle Time

Objectives

Problem without optimization

Matrix expression of a P-time event graph

Matrix expression of P-time event

graphs with interdependent residence durations

General form Ax <= b

Existence of a -periodic behavior

Conclusion

Chapter 4 Control with Specifications

Introduction

Time interval systems

(min, max, +) algebraic models

Timed event graphs

P-time event graphs

Time stream event graphs

Control synthesis

Problems

Pedagogical example: education system

Algebraic models

Fixed-point approach

Fixed-point formulation

Existence

Structure

Algorithm

Models

Fixed-point formulation

Optimal control with specifications

Initial conditions

Conclusion

Chapter 5 Online Aspect of Predictive Control

Introduction

Problem

Specific characteristics

Control without desired output (problem)

Objective

Example

Trajectory description

Relaxed system

Control with desired output (problem)

Fixed-point form

Relaxed system

Control on a sliding horizon (problem ): online and offline aspects

CPU time of the online control

Kleene star of the block tri-diagonal matrix and formal expressions of the sub-matrices

Conclusion

Bibliography

List of Symbols

Index