ISBN-10:
1848214618
ISBN-13:
9781848214613
Pub. Date:
12/26/2012
Publisher:
Wiley
Discrete Event Systems in Dioid Algebra and Conventional Algebra / Edition 1

Discrete Event Systems in Dioid Algebra and Conventional Algebra / Edition 1

by Philippe Declerck
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Product Details

ISBN-13: 9781848214613
Publisher: Wiley
Publication date: 12/26/2012
Series: FOCUS Series
Pages: 176
Product dimensions: 6.30(w) x 9.30(h) x 1.00(d)

About the Author

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

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Table of Contents

Chapter 1. Introduction  1

1.1. General introduction  1

1.2. History and three mainstays  2

1.3. Scientific context   2

1.3.1. Dioids   3

1.3.2. Petri nets   4

1.3.3. Time and algebraic models   5

1.4. Organization of the book   7

Chapter 2. Consistency   9

2.1. Introduction    9

2.1.1. Models   9

2.1.2. Physical point of view   11

2.1.3. Objectives   12

2.2. Preliminaries   14

2.3. Models and principle of the approach   17

2.3.1. P-time event graphs   17

2.3.2. Dater form   21

2.3.3. Principle of the approach (example 2)  23

2.4. Analysis in the “static” case  25

2.5. “Dynamic” model   28

2.6. Extremal acceptable trajectories by series ofmatrices    31

2.6.1. Lowest state trajectory   32

2.6.2. Greatest state trajectory  35

2.7. Consistency    36

2.7.1. Example 3   41

2.7.2. Maximal horizon of temporal consistency  44

2.7.3. Date of the first token deaths    47

2.7.4. Computational complexity   48

2.8. Conclusion   50

Chapter 3. Cycle Time   53

3.1. Objectives    53

3.2. Problem without optimization    55

3.2.1. Objective   55

3.2.2. Matrix expression of a P-time event graph  56

3.2.3. Matrix expression of P-time event graphs withinterdependent residence durations   57

3.2.4. General form Ax ≤ b   59

3.2.5. Example    60

3.2.6. Existence of a 1-periodic behavior   61

3.2.7. Example continued   65

3.3. Optimization    67

3.3.1. Approach 1   67

3.3.2. Example continued   69

3.3.3. Approach 2   70

3.4. Conclusion   75

3.5. Appendix    76

Chapter 4. Control with Specifications   79

4.1. Introduction    79

4.2. Time interval systems    80

4.2.1. (min, max, +) algebraic models   81

4.2.2. Timed event graphs   82

4.2.3. P-time event graphs   83

4.2.4. Time stream event graphs   84

4.3. Control synthesis   88

4.3.1. Problem    88

4.3.2. Pedagogical example: education system   89

4.3.3. Algebraic models    91

4.4. Fixed-point approach  92

4.4.1. Fixed-point formulation  92

4.4.2. Existence   95

4.4.3. Structure   103

4.5. Algorithm    107

4.6. Example    111

4.6.1. Models   111

4.6.2. Fixed-point formulation  113

4.6.3. Existence   114

4.6.4. Optimal control with specifications  116

4.6.5. Initial conditions    117

4.7. Conclusion   118

Chapter 5. Online Aspect of PredictiveControl    119

5.1. Introduction    119

5.1.1. Problem    119

5.1.2. Specific characteristics   120

5.2. Control without desired output (problem 1)  122

5.2.1. Objective   122

5.2.2. Example 1   123

5.2.3. Trajectory description   124

5.2.4. Relaxed system  125

5.3. Control with desired output (problem 2)  127

5.3.1. Objective   127

5.3.2. Fixed-point form  128

5.3.3. Relaxed system  129

5.4. Control on a sliding horizon (problem 3): online andoffline aspects   130

5.4.1. CPU time of the online control   131

5.5. Kleene star of the block tri-diagonal matrix and formalexpressions of the sub-matrices  132

5.6. Conclusion   138

Bibliography    141

List of Symbols    149

Index    153

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