Discrete, Continuous, and Hybrid Petri Nets

Transcription

1 Discrete, Continuous, and Hybrid Petri Nets Bearbeitet von René David, Hassane Alla 1. Auflage Buch. XXII, 570 S. Hardcover ISBN Format (B x L): 15,5 x 23,5 cm Gewicht: 2080 g Weitere Fachgebiete > Mathematik > Numerik und Wissenschaftliches Rechnen > Angewandte Mathematik, Mathematische Modelle schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.

2 Contents Foreword by Manuel Silva Preface Contents Notation V IX XIII XIX 1 Bases of Petri Nets BASIC CONCEPTS Places, Transitions, and Arcs Marking Firing of a Transition Autonomous and Non-Autonomous Petri Nets The Essential Characteristics SPECIAL PETRI NETS Particular Structures State Graph Event Graph Conflict Free Petri Net Free Choice Petri Net Simple Petri Net Pure Petri Net Abbreviations and Extensions Generalized Petri Nets Finite Capacity Petri Nets Colored Petri Nets Extended Petri Nets Priority Petri Nets Non-Autonomous Petri Nets Continuous and Hybrid Petri Nets Conclusion MODELING OF SOME CONCEPTS 17 NOTES and REFERENCES 20

3 XIV Content 2 Properties of Petri Nets PRESENTATION OF THE MAIN PROPERTIES Notations and Definitions Bounded Petri Net, Safe Petri Net Liveness and Deadlock Conflicts Invariants Conservative Component Repetitive Component SEEKING THE PROPERTIES OF PETRI NETS Graph of Markings and Coverability Root Tree Graph of Markings Coverability Root Tree Linear Algebra Notations and Definitions Fundamental Equation Conservative Components & Marking Invariants Repetitive Components & Firing Invariants Seeking P-invariants and T-invariants Reduction Methods Preserving Some Properties Other Results Strongly Connected Event Graphs Siphons and Traps Liveness Related to Other Properties Concluding Remarks Structuring Analysis Software 58 NOTES and REFERENCES 59 3 Non-Autonomous Petri Nets INTRODUCTION SYNCHRONIZED PETRI NETS Principle Iterated Firing On Occurrence of an External Event Elementary Firing Sequence Iterated Firing Properties of the Synchronized PNs Promptness or Stability Boundedness, Safeness, and Liveness Environment INTERPRETED PETRI NETS Definition of a Control Interpreted Petri Net Interpretation Algorithm of a Control Interpreted PN Interpreted PN Without Outputs: Generalization of the Concept of Synchronized PN 92

4 Content XV 3.4 TIMED PETRI NETS General Information Constant Timing P-Timed Petri Nets T-Timed Petri Nets Stationary Behavior Stochastic Petri Nets Basic Model Generalized Stochastic Petri Net Analysis and Simulation of Stochastic PNs 106 NOTES and REFERENCES Autonomous Continuous and Hybrid Petri Nets AUTONOMOUS CONTINUOUS PETRI NETS From Discrete Petri Net To Continuous Petri Net Definition Reachability and Conflicts Reachability Graph Firing Sequence and Reachability Space Conflicts AUTONOMOUS HYBRID PETRI NETS Intuitive presentation Definition Reachability and conflicts Reachability Graph Firing Sequence and Reachability Space Conflicts PROPERTIES OF AUTONOMOUS CONTINUOUS AND HYBRID PETRI NETS Definitions and Properties Similar for Discrete and Continuous Petri Nets Definitions Properties Reachability and Limit Reachability for a Continuous Petri Net ε-liveness for a Continuous Petri Net Lim-Liveness for a Continuous Petri Net Properties for a Hybrid Petri Net Similar Definitions and Properties Reachability and Liveness Incidence Matrix 142

5 XVI Content 4.4 EXTENDED HYBRID PETRI NETS Threshold Test Zero Test and Arc Weight Marking Definition 147 NOTES and REFERENCES Timed Continuous Petri Nets DEFINITION OF THE MODEL Limit Case of a Discrete Timed Petri Net Analysis of Some Basic Behaviors Sequences of Transitions, Same Maximal Speeds Sequences of Transitions, Different Maximal Speeds Synchronization Timed Continuous Petri Net With a Circuit Infinite Maximal Speed Definitions Definition and Notation Enabling Balance Evolution Graph CONFLICTS Existence of an Actual Conflict Conflict Resolution SPEED CALCULATION ALGORITHMS There is No Structural Conflict Resolution By Priorities Expected Results And Problems To Be Solved Setting Up the Set of Surely Firable Transitions Algorithm And Application Resolution By Sharings And Priorities Single Sharing Between Two Transitions One or Several Sharings Among Transitions Algorithm Complete Algorithm For All IB-states PROPERTIES Illustratory Examples A Simple Production System About Marking General Properties Modeling Power MAXIMAL SPEEDS FUNCTIONS OF TIME 214 NOTES and REFERENCES 216

6 Content XVII 6 Timed Hybrid Petri Nets DEFINITION OF THE MODEL Intuitive Presentation Events To Be Considered Conflict Resolutions Flow Rate and Maximal Firing Speed Formal Definitions Definition and Notations Enabling in Timed Hybrid Petri Nets Evolution Graph ALGORITHM Resolution for a Case 4 Conflict Resolution by Priority Resolution by Sharing Algorithmic Resolution Consequences of Various Events Timed Hybrid PNs Automatically Treated in Algorithm Hybrid PN Restricted to a Continuous PN Consistency of Resolution Rules Algorithm for Building the Evolution Graph Resolution of a Case Not Treated by Algorithm VARIANTS OF THE MODEL Synchronized D-Transitions Stochastic Timings for D-Transitions C-Transitions with Flow Rates Functions of Time EXTENDED TIMED HYBRID PETRI NETS Modeling of Zero Buffers Arc Weight 0 + for Testing if a C-Place is Empty Pure Delay of a Continuous Flow Simple Conveyor Various Behaviors of a Conveyor Fluid Example Conclusion on Timed Extended Hybrid Petri Nets 275 NOTES and REFERENCES Hybrid Petri Nets with Speeds Depending on the C-Marking APPROXIMATION OF TIMED DISCRETE SYSTEMS BY VHPNs Weakness of Basic Timed Hybrid PNs for Small Numbers Simple Cases of Variable Speed Hybrid PN General Case of VHPN Conflicts Definition of the Model Properties 293

7 XVIII Content Application Examples Example Example ASYMPTOTIC HYBRID PETRI NETS (AHPNs) A C-Transition Has a Single Input C-Place Constant Feeding Speed of Input C-Place Change of Feeding Speed of the Input C-Place Several Input C-Places Generalization Differences Between VHPN and AHPN Behaviors OTHER MODELS Liquid Flow Differential Hybrid Petri Nets Transfer Line with Operation-Dependent Failures 318 NOTES and REFERENCES 319 Postface 321 Appendices 327 A Regular Expressions and Languages 327 B Conflict Resolution 329 C Elements of Graph Theory 333 D Algebra of Events 335 E About Grafcet 339 F Modeling Power of Synchronized PNs 345 G Timed PNs Are Special Cases of Synchronized PNs 347 H Time Petri Nets 353 I Linearity of the Fundamental Equation for Continuous Petri Nets 357 J Notation 0 + and Non-Standard Analysis 361 K Sharing Between Two Transitions 363 L Graph of Relations Among Conflicts 369 M Piecewise Constant Maximal Speeds 373 N From Hybrid Petri Nets to Hybrid Automata 381 O P&T-Timed Petri Nets and Modeling Power 387 Exercises 393 Solutions to Exercises 433 References 501 Index 515