Skip to:Content
|
Bottom
Cover image for Discrete event systems in dioid algebra and conventional algebra
Title:
Discrete event systems in dioid algebra and conventional algebra
Personal Author:
Series:
Focus series in automation & control

Focus series in automation & control.
Publication Information:
London : ISTE ; Hoboken, NJ : Wiley, 2013.
Physical Description:
viii, 155 p. : ill. ; 24 cm.
ISBN:
9781848214613

Available:*

Library
Item Barcode
Call Number
Material Type
Item Category 1
Status
Searching...
30000010240328 QA402 D35 2013 Open Access Book Book
Searching...

On Order

Summary

Summary

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.


Author Notes

Philippe Declerck, LISA/ISTIA, University of Angers, France.


Table of Contents

Chapter 1 Introductionp. 1
1.1 General introductionp. 1
1.2 History and three mainstaysp. 2
1.3 Scientific contextp. 2
1.3.1 Dioidsp. 3
1.3.2 Petri netsp. 4
1.3.3 Time and algebraic modelsp. 5
1.4 Organization of the bookp. 7
Chapter 2 Consistencyp. 9
2.1 Introductionp. 9
2.1.1 Modelsp. 9
2.1.2 Physical point of viewp. 11
2.1.3 Objectivesp. 12
2.2 Preliminariesp. 14
2.3 Models and principle of the approachp. 17
2.3.1 P-time event graphsp. 17
2.3.2 Dater formp. 21
2.3.3 Principle of the approach (example 2)p. 23
2.4 Analysis in the "static" casep. 25
2.5 "Dynamic" modelp. 28
2.6 Extremal acceptable trajectories by series of matricesp. 31
2.6.1 Lowest state trajectoryp. 32
2.6.2 Greatest state trajectoryp. 35
2.7 Consistencyp. 36
2.7.1 Example 3p. 41
2.7.2 Maximal horizon of temporal consistencyp. 44
2.7.3 Date of the first token deathsp. 47
2.7.4 Computational complexityp. 48
2.8 Conclusionp. 50
Chapter 3 Cycle Timep. 53
3.1 Objectivesp. 53
3.2 Problem without optimizationp. 55
3.2.1 Objectivep. 55
3.2.2 Matrix expression of a P-time event graphp. 56
3.2.3 Matrix expression of P-time event graphs with interdependent residence durationsp. 57
3.2.4 General form Ax ≤ bp. 59
3.2.5 Examplep. 60
3.2.6 Existence of a 1-periodic behaviorp. 61
3.2.7 Example continuedp. 65
3.3 Optimizationp. 67
3.3.1 Approach 1p. 67
3.3.2 Example continuedp. 69
3.3.3 Approach 2p. 70
3.4 Conclusionp. 75
3.5 Appendixp. 76
Chapter 4 Control with Specificationsp. 79
4.1 Introductionp. 79
4.2 Time interval systemsp. 80
4.2.1 (min, max, +) algebraic modelsp. 81
4.2.2 Timed event graphsp. 82
4.2.3 P-time event graphsp. 83
4.2.4 Time stream event graphsp. 84
4.3 Control synthesisp. 88
4.3.1 Problemp. 88
4.3.2 Pedagogical example: education systemp. 89
4.3.3 Algebraic modelsp. 91
4.4 Fixed-point approachp. 92
4.4.1 Fixed-point formulationp. 92
4.4.2 Existencep. 95
4.4.3 Structurep. 103
4.5 Algorithmp. 107
4.6 Examplep. 111
4.6.1 Modelsp. 111
4.6.2 Fixed-point formulationp. 113
4.6.3 Existencep. 114
4.6.4 Optimal control with specificationsp. 116
4.6.5 Initial conditionsp. 117
4.7 Conclusionp. 118
Chapter 5 Online Aspect of Predictive Controlp. 119
5.1 Introductionp. 119
5.1.1 Problemp. 119
5.1.2 Specific characteristicsp. 120
5.2 Control without desired output (problem 1)p. 122
5.2.1 Objectivep. 122
5.2.2 Example 1p. 123
5.2.3 Trajectory descriptionp. 124
5.2.4 Relaxed systemp. 125
5.3 Control with desired output (problem 2)p. 127
5.3.1 Objectivep. 127
5.3.2 Fixed-point formp. 128
5.3.3 Relaxed systemp. 129
5.4 Control on a sliding horizon (problem 3): online and offline aspectsp. 130
5.4.1 CPU time of the online controlp. 131
5.5 Kleene star of the block tri-diagonal matrix and formal expressions of the sub-matricesp. 132
5.6 Conclusionp. 138
Bibliographyp. 141
List of Symbolsp. 149
Indexp. 153
Go to:Top of Page