Discrete, Continuous, And Hybrid Petri Nets,9783540224808

Discrete, Continuous, And Hybrid Petri Nets

by ;
ISBN13: 9783540224808
ISBN10: 3540224807
Format: Hardcover
Pub. Date: 2004-12-01
Publisher(s): Springer Verlag
List Price: $187.95

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Summary

This monograph presents a well written and clearly organized introduction in the standard methods of discrete, continuous and hybrid Petri Nets. Starting from the basics of Petri Nets the book imparts an accurate understanding of continuous and hybrid Petri Nets. Preserving the consistency of basic concepts throughout the text it introduces a unified framework for all the models presented. The book is a scientific monograph as well as a didactic tutorial which is easy to understand due to many exercises with solutions, detailed figures and several case studies. It demonstrates that Petri nets are a deep, practical and alive field important for researchers, engineers and graduate students in engineering and computer science.

Table of Contents

Foreword v
Manuel Silva
Preface ix
Contents xiii
Notation xix
Bases of Petri Nets
1(20)
Basic Concepts
1(4)
Places, Transitions, and Arcs
1(1)
Marking
2(1)
Firing of a Transition
3(1)
Autonomous and Non-Autonomous Petri Nets
4(1)
The Essential Characteristics
5(1)
Special Petri Nets
5(12)
Particular Structures
6(1)
State Graph
7(1)
Event Graph
7(1)
Conflict Free Petri Net
8(1)
Free Choice Petri Net
8(1)
Simple Petri Net
8(1)
Pure Petri Net
9(1)
Abbreviations and Extensions
9(1)
Generalized Petri Nets
9(2)
Finite Capacity Petri Nets
11(1)
Colored Petri Nets
12(1)
Extended Petri Nets
13(2)
Priority Petri Nets
15(1)
Non-Autonomous Petri Nets
16(1)
Continuous and Hybrid Petri Nets
17(1)
Conclusion
17(1)
Modeling of Some Concepts
17(4)
Notes and References
20(1)
Properties of Petri Nets
21(40)
Presentation of the Main Properties
21(16)
Notations and Definitions
21(3)
Bounded Petri Net, Safe Petri Net
24(1)
Liveness and Deadlock
25(5)
Conflicts
30(4)
Invariants
34(1)
Conservative Component
34(1)
Repetitive Component
35(2)
Seeking the Properties of Petri Nets
37(24)
Graph of Markings and Coverability Root Tree
37(1)
Graph of Markings
38(1)
Coverability Root Tree
39(2)
Linear Algebra
41(1)
Notations and Definitions
41(3)
Fundamental Equation
44(2)
Conservative Components & Marking Invariants
46(3)
Repetitive Components & Firing Invariants
49(1)
Seeking P-invariants and T-invariants
50(1)
Reduction Methods Preserving Some Properties
51(2)
Other Results
53(1)
Strongly Connected Event Graphs
53(1)
Siphons and Traps
54(1)
Liveness Related to Other Properties
55(1)
Concluding Remarks
56(1)
Structuring
57(1)
Analysis Software
58(1)
Notes and References
59(2)
Non-Autonomous Petri Nets
61(50)
Introduction
61(2)
Synchronized Petri Nets
63(21)
Principle
64(6)
Iterated Firing On Occurrence of an External Event
70(1)
Elementary Firing Sequence
70(3)
Iterated Firing
73(3)
Properties of the Synchronized PNs
76(1)
Promptness or Stability
76(3)
Boundedness, Safeness, and Liveness
79(3)
Environment
82(2)
Interpreted Petri Nets
84(9)
Definition of a Control Interpreted Petri Net
85(4)
Interpretation Algorithm of a Control Interpreted PN
89(3)
Interpreted PN Without Outputs: Generalization of the Concept of Synchronized PN
92(1)
Timed Petri Nets
93(18)
General Information
93(3)
Constant Timing
96(1)
P-Timed Petri Nets
96(2)
T-Timed Petri Nets
98(3)
Stationary Behavior
101(2)
Stochastic Petri Nets
103(1)
Basic Model
103(2)
Generalized Stochastic Petri Net
105(1)
Analysis and Simulation of Stochastic PNs
106(2)
Notes and References
108(3)
Autonomous Continuous and Hybrid Petri Nets
111(38)
Autonomous Continuous Petri Nets
111(11)
From Discrete Petri Net to Continuous Petri Net
111(3)
Definition
114(2)
Reachability and Conflicts
116(1)
Reachability Graph
116(3)
Firing Sequence and Reachability Space
119(2)
Conflicts
121(1)
Autonomous Hybrid Petri Nets
122(11)
Intuitive presentation
122(2)
Definition
124(2)
Reachability and conflicts
126(1)
Reachability Graph
127(3)
Firing Sequence and Reachability Space
130(2)
Conflicts
132(1)
Properties of Autonomous Continuous and Hybrid Petri Nets
133(10)
Definitions and Properties Similar for Discrete and Continuous Petri Nets
133(1)
Definitions
133(1)
Properties
134(1)
Reachability and Limit Reachability for a Continuous Petri Net
135(3)
ε-Liveness for a Continuous Petri Net
138(1)
Lim-Liveness for a Continuous Petri Net
139(2)
Properties for a Hybrid Petri Net
141(1)
Similar Definitions and Properties
141(1)
Reachability and Liveness
141(1)
Incidence Matrix
142(1)
Extended Hybrid Petri Nets
143(6)
Threshold Test
143(1)
Zero Test and Arc Weight 0+
144(2)
Marking 0+
146(1)
Definition
147(1)
Notes and References
148(1)
Timed Continuous Petri Nets
149(70)
Definition of the Model
149(21)
Limit Case of a Discrete Timed Petri Net
150(1)
Analysis of Some Basic Behaviors
151(1)
Sequences of Transitions, Same Maximal Speeds
152(4)
Sequences of Transitions, Different Maximal Speeds
156(3)
Synchronization
159(1)
Timed Continuous Petri Net With a Circuit
160(1)
Infinite Maximal Speed
161(2)
Definitions
163(1)
Definition and Notation
164(1)
Enabling
164(3)
Balance
167(2)
Evolution Graph
169(1)
Conflicts
170(3)
Existence of an Actual Conflict
170(1)
Conflict Resolution
171(2)
Speed Calculation Algorithms
173(32)
There is No Structural Conflict
174(2)
Resolution By Priorities
176(1)
Expected Results And Problems To Be Solved
176(4)
Setting Up the Set of Surely Firable Transitions
180(5)
Algorithm And Application
185(4)
Resolution By Sharings And Priorities
189(1)
Single Sharing Between Two Transitions
189(2)
One or Several Sharings Among Transitions
191(6)
Algorithm
197(5)
Complete Algorithm For All IB-states
202(3)
Properties
205(9)
Illustratory Examples
205(1)
A Simple Production System
205(2)
About Marking 0+
207(1)
General Properties
208(4)
Modeling Power
212(2)
Maximal Speeds Functions of Time
214(5)
Notes and References
216(3)
Timed Hybrid Petri Nets
219(60)
Definition of the Model
219(16)
Intuitive Presentation
220(1)
Events To Be Considered
221(2)
Conflict Resolutions
223(3)
Flow Rate and Maximal Firing Speed
226(2)
Formal Definitions
228(1)
Definition and Notations
228(2)
Enabling in Timed Hybrid Petri Nets
230(2)
Evolution Graph
232(3)
Algorithm
235(20)
Resolution for a Case 4 Conflict
236(1)
Resolution by Priority
236(2)
Resolution by Sharing
238(2)
Algorithmic Resolution
240(1)
Consequences of Various Events
241(2)
Timed Hybrid PNs Automatically Treated in Algorithm 6.1
243(1)
Hybrid PN Restricted to a Continuous PN
243(2)
Consistency of Resolution Rules
245(4)
Algorithm for Building the Evolution Graph
249(5)
Resolution of a Case Not Treated by Algorithm 6.1
254(1)
Variants of the Model
255(6)
Synchronized D-Transitions
255(3)
Stochastic Timings for D-Transitions
258(1)
C-Transitions with Flow Rates Functions of Time
259(2)
Extended Timed Hybrid Petri Nets
261(18)
Modeling of Zero Buffers
262(3)
Arc Weight 0+ for Testing if a C-Place is Empty
265(3)
Pure Delay of a Continuous Flow
268(1)
Simple Conveyor
268(4)
Various Behaviors of a Conveyor
272(2)
Fluid Example
274(1)
Conclusion on Timed Extended Hybrid Petri Nets
275(1)
Notes and References
276(3)
Hybrid Petri Nets with Speeds Depending on the C-Marking
279(42)
Approximation of Timed Discrete Systems by VHPNs
279(20)
Weakness of Basic Timed Hybrid PNs for Small Numbers
280(1)
Simple Cases of Variable Speed Hybrid PN
281(4)
General Case of VHPN
285(1)
Conflicts
285(2)
Definition of the Model
287(6)
Properties
293(1)
Application Examples
294(1)
Example 1
294(2)
Example 2
296(3)
Asymptotic Hybrid Petri Nets (AHPNs)
299(15)
A C-Transition Has a Single Input C-Place
300(1)
Constant Feeding Speed of Input C-Place
300(3)
Change of Feeding Speed of the Input C-Place
303(2)
Several Input C-Places
305(1)
Generalization
306(4)
Differences Between VHPN and AHPN Behaviors
310(4)
Other Models
314(7)
Liquid Flow
314(1)
Differential Hybrid Petri Nets
315(3)
Transfer Line with Operation-Dependent Failures
318(1)
Notes and References
319(2)
Postface
321(6)
Appendices
327(66)
A Regular Expressions and Languages
327(2)
B Conflict Resolution
329(4)
C Elements of Graph Theory
333(2)
D Algebra of Events
335(4)
E About Grafcet
339(6)
F Modeling Power of Synchronized PNs
345(2)
G Timed PNs Are Special Cases of Synchronized PNs
347(6)
H Time Petri Nets
353(4)
I Linearity of the Fundamental Equation for Continuous Petri Nets
357(4)
J Notation 0+ and Non-Standard Analysis
361(2)
K Sharing Between Two Transitions
363(6)
L Graph of Relations Among Conflicts
369(4)
M Piecewise Constant Maximal Speeds
373(8)
N From Hybrid Petri Nets to Hybrid Automata
381(6)
O P&T-Timed Petri Nets and Modeling Power
387(6)
Exercises 393(40)
Solutions to Exercises 433(68)
References 501(14)
Index 515

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