David / Alla Discrete, Continuous, and Hybrid Petri Nets

2. Auflage 2010
ISBN: 978-3-642-10669-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 550 Seiten

Petri Nets were introduced and still successfully used to analyze and model discrete event systems especially in engineering and computer sciences such as in automatic control. Recently this discrete Petri Nets formalism was successfully extended to continuous and hybrid systems. This monograph presents a well written and clearly organized introduction in the standard methods of Petri Nets with the aim to reach an accurate understanding of continuous and hybrid Petri Nets, while preserving the consistency of basic concepts throughout the book. The book is a monograph as well as a didactic tool which is easy to understand due to many simple solved examples and detailed figures. In its second completely reworked edition various sections, concepts and recently developed algorithms are added as well as additional examples/exercises.

Autoren/Hrsg.

David, René

Alla, Hassane

Inhaltsverzeichnis

1;Foreword;4
2;Preface;7
3;Contents;11
4;Notation;17
5;Bases of Petri Nets;21
5.1;BASIC CONCEPTS;21
5.1.1;Places, Transitions and Arcs;21
5.1.2;Marking;22
5.1.3;Firing of a Transition;23
5.1.4;Autonomous and Non-autonomous Petri Nets;24
5.1.5;The Essential Characteristics;25
5.2;SPECIAL PETRI NETS;25
5.2.1;Particular Structures;26
5.2.2;Abbreviations and Extensions;29
5.3;MODELING OF SOME CONCEPTS;37
6;Properties of Petri Nets;41
6.1;PRESENTATION OF THE MAIN PROPERTIES;41
6.1.1;Notations and Definitions;41
6.1.2;Bounded Petri Net, Safe Petri Net;44
6.1.3;Liveness and Deadlock;45
6.1.4;Conflicts;50
6.1.5;Invariants;54
6.2;SEEKING THE PROPERTIES OF PETRI NETS;57
6.2.1;Graph of Markings and Coverability Root Tree;58
6.2.2;Linear Algebra;62
6.2.3;Reduction Methods Preserving Some Properties;72
6.2.4;Other Results;73
6.2.5;Concluding Remarks;77
7;Non-Autonomous Petri Nets;81
7.1;INTRODUCTION;81
7.2;SYNCHRONIZED PETRI NETS;83
7.2.1;Principle;84
7.2.2;Iterated Firing On Occurrence of an External Event;90
7.2.3;Properties of the Synchronized PNs;99
7.3;INTERPRETED PETRI NETS;108
7.3.1;Definition of a Control Interpreted Petri Net;109
7.3.2;Interpretation Algorithm of a Control Interpreted PN;113
7.3.3;Interpreted PN Without Outputs: Generalization of the Concept of Synchronized PN;116
7.4;TIMED PETRI NETS;118
7.4.1;General Information;118
7.4.2;Constant Timing;121
7.4.3;Stochastic Petri Nets;129
8;Autonomous Continuous and Hybrid Petri Nets;137
8.1;MOTIVATION;137
8.2;AUTONOMOUS CONTINUOUS PETRI NETS;139
8.2.1;From Discrete Petri Net To Continuous Petri Net;139
8.2.2;Definition;141
8.2.3;Reachability and Conflicts;143
8.2.4;Comments about units;149
8.3;AUTONOMOUS HYBRID PETRI NETS;150
8.3.1;Intuitive presentation;151
8.3.2;Definition;154
8.3.3;Reachability and conflicts;157
8.4;PROPERTIES OF AUTONOMOUS CONTINUOUS AND HYBRID PETRI NETS;163
8.4.1;Definitions and Properties Similar for Discrete and Continuous Petri Nets;163
8.4.2;Reachability and Limit Reachability for a Continuous Petri Net;165
8.4.3;e-Liveness for a Continuous Petri Net;168
8.4.4;Lim-Liveness for a Continuous Petri Net;169
8.4.5;Properties for a Hybrid Petri Net;171
8.5;EXTENDED HYBRID PETRI NETS;173
8.5.1;Threshold Test;173
8.5.2;Zero Test and Arc Weight 0+;174
8.5.3;Marking 0+;176
8.5.4;Definition;177
9;Timed Continuous Petri Nets;179
9.1;DEFINITION OF THE MODEL;179
9.1.1;Limit Case of a Discrete Timed Petri Net;180
9.1.2;Analysis of Some Basic Behaviors;181
9.1.3;Definitions;194
9.2;CONFLICTS;200
9.2.1;Existence of an Actual Conflict;200
9.2.2;Conflict Resolution;202
9.3;SPEED CALCULATION ALGORITHMS;204
9.3.1;There is No Structural Conflict;205
9.3.2;Resolution By Priorities;207
9.3.3;Resolution By Sharings And Priorities;220
9.3.4;Complete Algorithm For All IB-states;233
9.4;PROPERTIES;236
9.4.1;Illustratory Examples;236
9.4.2;General Properties;240
9.4.3;Modeling Power;243
9.5;MAXIMAL SPEEDS FUNCTIONS OF TIME;245
10;Timed Hybrid Petri Nets;250
10.1;DEFINITION OF THE MODEL;250
10.1.1;Flow Rate and Maximal Firing Speed;251
10.1.2;Illustrative Example;254
10.1.3;Events To Be Considered;256
10.1.4;Conflict Resolutions;257
10.1.5;Formal Definitions;260
10.2;ALGORITHM;267
10.2.1;Resolution for a Case 4 Conflict;268
10.2.2;Consequences of Various Events;273
10.2.3;Timed Hybrid PNs Automatically Treated in Algorithm 6.1;275
10.2.4;Algorithm for Building the Evolution Graph;281
10.2.5;Resolution of a Case Not Treated by Algorithm 6.1;287
10.3;VARIANTS OF THE MODEL;288
10.3.1;Synchronized D-Transitions;289
10.3.2;Stochastic Timings for D-Transitions;292
10.3.3;Hybrid Petri Nets with Time Transitions;293
10.3.4;C-Transitions with Flow Rates Functions of Time;294
10.3.5;Colored Hybrid Petri Net;296
10.4;EXTENDED TIMED HYBRID PETRI NETS;297
10.4.1;Modeling of Zero Buffers;298
10.4.2;Arc Weight 0+ for Testing if a C-Place is Empty;301
10.4.3;Pure Delay of a Continuous Flow;304
10.4.4;Conclusion on Timed Extended Hybrid Petri Nets;311
11;Hybrid Petri Nets with Speeds Depending on the C-Marking;314
11.1;APPROXIMATION OF TIMED DISCRETE SYSTEMS BY VHPNs;314
11.1.1;Weakness of Basic Timed Hybrid PNs for Small Numbers;315
11.1.2;Simple Cases of Variable Speed Hybrid PN;316
11.1.3;General Case of VHPN;320
11.1.4;Application Examples;329
11.2;ASYMPTOTIC HYBRID PETRI NETS (AHPNs);335
11.2.1;A C-Transition Has a Single Input C-Place;335
11.2.2;Several Input C-Places;340
11.2.3;Generalization;342
11.2.4;Differences Between VHPN and AHPN Behaviors;345
11.3;OTHER MODELS;349
11.3.1;Liquid Flow;349
11.3.2;Differential Hybrid Petri Nets;350
11.3.3;Transfer Line with Operation-Dependent Failures;354
12;Postface;357
13;Appendix;363
13.1;Regular Expressions and Languages;363
13.2;Conflict Resolution;365
13.3;Elements of Graph Theory;369
13.4;Algebra of Events;371
13.5;About Grafcet;375
13.6;Modeling Power of Synchronized PNs;381
13.7;Timed Petri Nets Are Special Cases of Synchronized Petri Nets;383
13.8;Time Petri Nets;389
13.9;Linearity of the Fundamental Equation for Continuous Petri Nets;393
13.10;Notation 0+ and Non-Standard Analysis;397
13.11;Sharing Between Two Transitions;399
13.12;Graph of Relations Among Conflicts;405
13.13;Piecewise Constant Maximal Speeds;409
13.14;From Hybrid PNs to Hybrid Automata;417
13.15;P&T-Timed Petri Nets and Modeling Power;423
14;Exercises;429
15;Solutions to Exercises;470
16;References;542
17;Index;558