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E-raamat: Discrete Event Systems in Dioid Algebra and Conventional Algebra

  • Formaat: PDF+DRM
  • Ilmumisaeg: 13-Feb-2013
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118579657
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Discrete Event Systems in Dioid Algebra and Conventional AlgebraSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 13-Feb-2013
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118579657
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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.

Chapter 1 Introduction
1(8)
1.1 General introduction
1(1)
1.2 History and three mainstays
2(1)
1.3 Scientific context
2(5)
1.3.1 Dioids
3(1)
1.3.2 Petri nets
4(1)
1.3.3 Time and algebraic models
5(2)
1.4 Organization of the book
7(2)
Chapter 2 Consistency
9(44)
2.1 Introduction
9(5)
2.1.1 Models
9(2)
2.1.2 Physical point of view
11(1)
2.1.3 Objectives
12(2)
2.2 Preliminaries
14(3)
2.3 Models and principle of the approach
17(8)
2.3.1 P-time event graphs
17(4)
2.3.2 Dater form
21(2)
2.3.3 Principle of the approach (example 2)
23(2)
2.4 Analysis in the "static" case
25(3)
2.5 "Dynamic" model
28(3)
2.6 Extremal acceptable trajectories by series of matrices
31(5)
2.6.1 Lowest state trajectory
32(3)
2.6.2 Greatest state trajectory
35(1)
2.7 Consistency
36(14)
2.7.1 Example 3
41(3)
2.7.2 Maximal horizon of temporal consistency
44(3)
2.7.3 Date of the first token deaths
47(1)
2.7.4 Computational complexity
48(2)
2.8 Conclusion
50(3)
Chapter 3 Cycle Time
53(26)
3.1 Objectives
53(2)
3.2 Problem without optimization
55(12)
3.2.1 Objective
55(1)
3.2.2 Matrix expression of a P-time event graph
56(1)
3.2.3 Matrix expression of P-time event graphs with interdependent residence durations
57(2)
3.2.4 General form Ax ≤ b
59(1)
3.2.5 Example
60(1)
3.2.6 Existence of a 1-periodic behavior
61(4)
3.2.7 Example continued
65(2)
3.3 Optimization
67(8)
3.3.1 Approach 1
67(2)
3.3.2 Example continued
69(1)
3.3.3 Approach 2
70(5)
3.4 Conclusion
75(1)
3.5 Appendix
76(3)
Chapter 4 Control with Specifications
79(40)
4.1 Introduction
79(1)
4.2 Time interval systems
80(8)
4.2.1 (min, max, +) algebraic models
81(1)
4.2.2 Timed event graphs
82(1)
4.2.3 P-time event graphs
83(1)
4.2.4 Time stream event graphs
84(4)
4.3 Control synthesis
88(4)
4.3.1 Problem
88(1)
4.3.2 Pedagogical example: education system
89(2)
4.3.3 Algebraic models
91(1)
4.4 Fixed-point approach
92(15)
4.4.1 Fixed-point formulation
92(3)
4.4.2 Existence
95(8)
4.4.3 Structure
103(4)
4.5 Algorithm
107(4)
4.6 Example
111(7)
4.6.1 Models
111(2)
4.6.2 Fixed-point formulation
113(1)
4.6.3 Existence
114(2)
4.6.4 Optimal control with specifications
116(1)
4.6.5 Initial conditions
117(1)
4.7 Conclusion
118(1)
Chapter 5 Online Aspect of Predictive Control
119(22)
5.1 Introduction
119(3)
5.1.1 Problem
119(1)
5.1.2 Specific characteristics
120(2)
5.2 Control without desired output (problem 1)
122(5)
5.2.1 Objective
122(1)
5.2.2 Example 1
123(1)
5.2.3 Trajectory description
124(1)
5.2.4 Relaxed system
125(2)
5.3 Control with desired output (problem 2)
127(3)
5.3.1 Objective
127(1)
5.3.2 Fixed-point form
128(1)
5.3.3 Relaxed system
129(1)
5.4 Control on a sliding horizon (problem 3): online and offline aspects
130(2)
5.4.1 CPU time of the online control
131(1)
5.5 Kleene star of the block tri-diagonal matrix and formal expressions of the sub-matrices
132(6)
5.6 Conclusion
138(3)
Bibliography 141(8)
List of Symbols 149(4)
Index 153
Philippe Declerck is Senior Lecturer LISA / ISTIA Laboratory at University of Angers, France.
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