Discrete, Continuous, And Hybrid Petri Nets

René David, Hassane Alla

Springer, 2005 - Technology & Engineering - 524 pages

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.

Contents

• Bases of Petri Nets: 1
• 112 Marking: 2
• 113 Firing of a Transition: 3
• 114 Autonomous and Nonautonomous Petri Nets: 4
• 115 The Essential Characteristics: 5
• 121 Particular Structures: 6
• 1211 State Graph: 7
• 1213 Conflict Free Petri Net: 8
• 1216 Pure Petri Net: 9
• 1222 Finite Capacity Petri Nets: 11
• 1223 Colored Petri Nets: 12
• 1224 Extended Petri Nets: 13
• 7225 Priority Petri Nets: 15
• 1226 Nonautonomous Petri Nets: 16
• 1227 Continuous and Hybrid Petri Nets: 17
• NOTES and REFERENCES: 20
• Properties of Petri Nets: 21
• 212 Bounded Petri Net Safe Petri Net: 24
• 213 Liveness and Deadlock: 25
• 214 Conflicts: 30
• 215 Invariants: 34
• 2152 Repetitive Component: 35
• 22 SEEKING THE PROPERTIES OF PETRI NETS: 37
• 2211 Graph of Markings: 38
• 2212 Coverability Root Tree: 39
• 222 Linear Algebra: 41
• 2222 Fundamental Equation: 44
• 2223 Conservative Components Marking Invariants: 46
• 2224 Repetitive Components Firing Invariants: 49
• 2225 Seeking Pinvariants and Tinvariants: 50
• 223 Reduction Methods Preserving Some Properties: 51
• 224 Other Results: 53
• 2242 Siphons and Traps: 54
• 2243 Liveness Related to Other Properties: 55
• 225 Concluding Remarks: 56
• 2251 Structuring: 57
• 2252 Analysis Software: 58
• NOTES and REFERENCES: 59
• NonAutonomous Petri Nets: 61
• 32 SYNCHRONIZED PETRI NETS: 63
• 321 Principle: 64
• 322 Iterated Firing On Occurrence of an External Event: 70
• 3222 Iterated Firing: 73
• 323 Properties of the Synchronized PNs: 76
• 3232 Boundedness Safeness and Liveness: 79
• 3233 Environment: 82
• 33 INTERPRETED PETRI NETS: 84
• 331 Definition of a Control Interpreted Petri Net: 85
• 332 Interpretation Algorithm of a Control Interpreted PN: 89
• Generalization of the Concept of Synchronized PN: 92
• 34 TIMED PETRI NETS: 93
• 342 Constant Timing: 96
• 3422 TTimed Petri Nets: 98
• 3423 Stationary Behavior: 101
• 343 Stochastic Petri Nets: 103
• 3432 Generalized Stochastic Petri Net: 105
• 3433 Analysis and Simulation of Stochastic Petri Nets: 106
• NOTES and REFERENCES: 108
• Autonomous Continuous and Hybrid Petri Nets: 111
• 412 Definition: 114
• 413 Reachability and Conflicts: 116
• 4132 Firing Sequence and Reachability Space: 119
• 4133 Conflicts: 121
• 42 AUTONOMOUS HYBRID PETRI NETS: 122
• 422 Definition: 124
• 423 Reachability and conflicts: 126
• 4231 Reachability Graph: 127
• 4232 Firing Sequence and Reachability Space: 130
• 4233 Conflicts: 132
• 43 PROPERTIES OF AUTONOMOUS CONTINUOUS AND HYBRID PETRI NETS: 133
• 4312 Properties: 134
• 432 Reachability and Limit Reachability for a Continuous Petri Net: 135
• 433 eLiveness for a Continuous Petri Net: 138
• 434 LimLiveness for a Continuous Petri Net: 139
• 435 Properties for a Hybrid Petri Net: 141
• 4353 Incidence Matrix: 142
• 44 EXTENDED HYBRID PETRI NETS: 143
• 442 Zero Test and Arc Weight 0+: 144
• 443 Marking 0+: 146
• 444 Definition: 147
• NOTES and REFERENCES: 148
• Timed Continuous Petri Nets: 149
• 511 Limit Case of a Discrete Timed Petri Net: 150
• 512 Analysis of Some Basic Behaviors: 151
• 5121 Sequences of Transitions Same Maximal Speeds: 152
• 5122 Sequences of Transitions Different Maximal Speeds: 156
• 5123 Synchronization: 159
• 5124 Timed Continuous Petri Net With a Circuit: 160
• 5125 Infinite Maximal Speed: 161
• 513 Definitions: 163
• 5131 Definition and Notation: 164
• 5133 Balance: 167
• 5134 Evolution Graph: 169
• 52 CONFLICTS: 170
• 522 Conflict Resolution: 171
• 53 SPEED CALCULATION ALGORITHMS: 173
• 531 There is No Structural Conflict: 174
• 532 Resolution By Priorities: 176
• 5322 Setting Up the Set of Surely Firable Transitions: 180
• 5323 Algorithm And Application: 185
• 533 Resolution By Sharings And Priorities: 189
• 5332 One or Several Sharings Among Transitions: 191
• 5333 Algorithm: 197
• 534 Complete Algorithm For All IBstates: 202
• 54 PROPERTIES: 205
• 5412 About Marking 0+: 207
• 542 General Properties: 208
• 543 Modeling Power: 212
• 55 MAXIMAL SPEEDS FUNCTIONS OF TIME: 214
• NOTES and REFERENCES: 216
• Timed Hybrid Petri Nets: 219
• 611 Intuitive Presentation: 220
• 612 Events To Be Considered: 221
• 613 Conflict Resolutions: 223
• 614 Flow Rate and Maximal Firing Speed: 226
• 615 Formal Definitions: 228
• 6152 Enabling in Timed Hybrid Petri Nets: 230
• 6153 Evolution Graph: 232
• 62 ALGORITHM: 235
• 621 Resolution for a Case 4 Conflict: 236
• 6212 Resolution by Sharing: 238
• 6213 Algorithmic Resolution: 240
• 622 Consequences of Various Events: 241
• 623 Timed Hybrid PNs Automatically Treated in Algorithm 61: 243
• 6232 Consistency of Resolution Rules: 245
• 624 Algorithm for Building the Evolution Graph: 249
• 625 Resolution of a Case Not Treated by Algorithm 61: 254
• 63 VARIANTS OF THE MODEL: 255
• 632 Stochastic Timings for DTransitions: 258
• 633 CTransitions with Flow Rates Functions of Time: 259
• 64 EXTENDED TIMED HYBRID PETRI NETS: 261
• 641 Modeling of Zero Buffers: 262
• 642 Arc Weight 0+ for Testing if a CPlace is Empty: 265
• 643 Pure Delay of a Continuous Flow: 268
• 6432 Various Behaviors of a Conveyor: 272
• 6433 Fluid Example: 274
• 644 Conclusion on Timed Extended Hybrid Petri Nets: 275
• NOTES and REFERENCES: 276
• Hybrid Petri Nets with Speeds Depending on the CMarking: 279
• 711 Weakness of Basic Timed Hybrid PNs for Small Numbers: 280
• 712 Simple Cases of Variable Speed Hybrid PN: 281
• 713 General Case of VHPN: 285
• 7132 Definition of the Model: 287
• 7133 Properties: 293
• 714 Application Examples: 294
• 7142 Example 2: 296
• 72 ASYMPTOTIC HYBRID PETRI NETS AHPNs: 299
• 721 A C Transition Has a Single Input CPlace: 300
• 7212 Change of Feeding Speed of the Input CPlace: 303
• 722 Several Input CPlaces: 305
• 723 Generalization: 306
• 724 Differences Between VHPN and AHPN Behaviors: 310
• 73 OTHER MODELS: 314
• 732 Differential Hybrid Petri Nets: 315
• 733 Transfer Line with OperationDependent Failures: 318
• NOTES and REFERENCES: 319
• Postface: 321
• Regular Expressions and Languages: 327
• Conflict Resolution: 329
• Elements of Graph Theory: 333
• Algebra of Events: 335
• About Grafcet: 339
• Modeling Power of Synchronized PNs: 345
• Timed Petri Nets Are Special Cases of Synchronized Petri Nets: 347
• Time Petri Nets: 353
• Linearity of the Fundamental Equation for Continuous Petri Nets: 357
• Notation 0+ and NonStandard Analysis: 361
• Sharing Between Two Transitions: 363
• Graph of Relations Among Conflicts: 369
• Piecewise Constant Maximal Speeds: 373
• From Hybrid PNs to Hybrid Automata: 381
• PTTimed Petri Nets and Modeling Power: 387
• Exercises: 393
• Solutions to Exercises: 433
• References: 501
• Index: 515

About the author

David is a former member of the Faculte de droit et des sciences sociales de Paris and is presently affiliated with the Universite d'Aix-Merseille.

Bibliographic information

• Title: Discrete, Continuous, And Hybrid Petri Nets
• Authors: René David, Hassane Alla
• Edition: illustrated
• Publisher: Springer, 2005
• ISBN: 3540224807, 9783540224808
• Length: 524 pages
• Subjects: Technology & Engineering / Engineering (General)