<p> <br/></p><p>作者：David 作者：Rene/ Alla 作者：Hassane  </p><li>出版社：Springer Verlag  </li><li>ISBN号：354022480  </li><li>页数：524  </li><li>出版日期：2004-01-12  </li><p>Foreword by Manuel Silva V<br/>Preface IX<br/>Contents XIII<br/>Notation XIX<br/>1 Bases of Petri Nets 1<br/>1.1 BASIC CONCEPTS 1<br/>1.1.1 Places, Transitions, and Arcs 1<br/>1.1.2 Marking 2<br/>1.1.3 Firing of a Transition 3<br/>1.1.4 Autonomous and Non-Autonomous Petri Nets 4<br/>1.1.5 The Essential Characteristics 5<br/>1.2 SPECIAL PETRI NETS 5<br/>1.2.1 Particular Structures 6<br/>1.2.1.1 State Graph 7<br/>1.2.1.2 Event Graph 7<br/>1.2.1.3 Conflict Free Petri Net 8<br/>1.2.1.4 Free Choice Petri Net 8<br/>1.2.1.5 Simple Petri Net 8<br/>1.2.1.6 Pure Petri Net 9<br/>1.2.2 Abbreviations and Extensions 9<br/>1.2.2.1 Generalized Petri Nets 9<br/>1.2.2.2 Finite Capacity Petri Nets 11<br/>1.2.2.3 Colored Petri Nets 12<br/>1.2.2.4 Extended Petri Nets 13<br/>1.2.2.5 Priority Petri Nets 15<br/>1.2.2.6 Non-Autonomous Petri Nets 16<br/>1.2.2.7 Continuous and Hybrid Petri Nets 17<br/>1.2.2.8 Conclusion 17<br/>1.3 MODELING OF SOME CONCEPTS 17<br/>NOTES and REFERENCES 20<br/>XIV Content<br/>2 Properties of Petri Nets 21<br/>2.1 PRESENTATION OF THE MAIN PROPERTIES 21<br/>2.1.1 Notations and Definitions 21<br/>2.1.2 Bounded Petri Net, Safe Petri Net 24<br/>2.1.3 Liveness and Deadlock 25<br/>2.1.4 Conflicts 30<br/>2.1.5 Invariants 34<br/>2.1.5.1 Conservative Component 34<br/>2.1.5.2 Repetitive Component 35<br/>2.2 SEEKING THE PROPERTIES OF PETRI NETS 37<br/>2.2.1 Graph of Markings and Coverability Root Tree 37<br/>2.2.1.1 Graph of Markings 38<br/>2.2.1.2 Coverability Root Tree 39<br/>2.2.2 Linear Algebra 41<br/>2.2.2.1 Notations and Definitions 41<br/>2.2.2.2 Fundamental Equation 44<br/>2.2.2.3 Conservative Components & Marking Invariants 46<br/>2.2.2.4 Repetitive Components & Firing Invariants 49<br/>2.2.2.5 Seeking P-invariants and T-invariants 50<br/>2.2.3 Reduction Methods Preserving Some Properties 51<br/>2.2.4 Other Results 53<br/>2.2.4.1 Strongly Connected Event Graphs 53<br/>2.2.4.2 Siphons and Traps 54<br/>2.2.4.3 Liveness Related to Other Properties 55<br/>2.2.5 Concluding Remarks 56<br/>2.2.5.1 Structuring 57<br/>2.2.5.2 Analysis Software 58<br/>NOTES and REFERENCES 59<br/>3 Non-Autonomous Petri Nets 61<br/>3.1 INTRODUCTION 61<br/>3.2 SYNCHRONIZED PETRI NETS 63<br/>3.2.1 Principle 64<br/>3.2.2 Iterated Firing On Occurrence of an External Event 70<br/>3.2.2.1 Elementary Firing Sequence 70<br/>3.2.2.2 Iterated Firing 73<br/>3.2.3 Properties of the Synchronized PNs 76<br/>3.2.3.1 Promptness or Stability 76<br/>3.2.3.2 Boundedness, Safeness, and Liveness 79<br/>3.2.3.3 Environment 82<br/>3.3 INTERPRETED PETRI NETS 84<br/>3.3.1 Definition of a Control Interpreted Petri Net 85<br/>3.3.2 Interpretation Algorithm of a Control Interpreted PN 89<br/>3.3.3 Interpreted PN Without Outputs: Generalization of the<br/>Concept of Synchronized PN 92<br/>Content XV<br/>3.4 TIMED PETRI NETS 93<br/>3.4.1 General Information 93<br/>3.4.2 Constant Timing 96<br/>3.4.2.1 P-Timed Petri Nets 96<br/>3.4.2.2 T-Timed Petri Nets 98<br/>3.4.2.3 Stationary Behavior 101<br/>3.4.3 Stochastic Petri Nets 103<br/>3.4.3.1 Basic Model 103<br/>3.4.3.2 Generalized Stochastic Petri Net 105<br/>3.4.3.3 Analysis and Simulation of Stochastic PNs 106<br/>NOTES and REFERENCES 108<br/>4 Autonomous Continuous and Hybrid Petri Nets 111<br/>4.1 AUTONOMOUS CONTINUOUS PETRI NETS 111<br/>4.1.1 From Discrete Petri Net To Continuous Petri Net 111<br/>4.1.2 Definition 114<br/>4.1.3 Reachability and Conflicts 116<br/>4.1.3.1 Reachability Graph 116<br/>4.1.3.2 Firing Sequence and Reachability Space 119<br/>4.1.3.3 Conflicts 121<br/>4.2 AUTONOMOUS HYBRID PETRI NETS 122<br/>4.2.1 Intuitive presentation 122<br/>4.2.2 Definition 124<br/>4.2.3 Reachability and conflicts 126<br/>4.2.3.1 Reachability Graph 127<br/>4.2.3.2 Firing Sequence and Reachability Space 130<br/>4.2.3.3 Conflicts 132<br/>4.3 PROPERTIES OF AUTONOMOUS CONTINUOUS AND<br/>HYBRID PETRI NETS 133<br/>4.3.1 Definitions and Properties Similar for Discrete and<br/>Continuous Petri Nets 133<br/>4.3.1.1 Definitions 133<br/>4.3.1.2 Properties 134<br/>4.3.2 Reachability and Limit Reachability for a Continuous<br/>Petri Net 135<br/>4.3.3 ε-Liveness for a Continuous Petri Net 138<br/>4.3.4 Lim-Liveness for a Continuous Petri Net 139<br/>4.3.5 Properties for a Hybrid Petri Net 141<br/>4.3.5.1 Similar Definitions and Properties 141<br/>4.3.5.2 Reachability and Liveness 141<br/>4.3.5.3 Incidence Matrix 142<br/>XVI Content<br/>4.4 EXTENDED HYBRID PETRI NETS 143<br/>4.4.1 Threshold Test 143<br/>4.4.2 Zero Test and Arc Weight 0+ 144<br/>4.4.3 Marking 0+ 146<br/>4.4.4 Definition 147<br/>NOTES and REFERENCES 148<br/>5 Timed Continuous Petri Nets 149<br/>5.1 DEFINITION OF THE MODEL 149<br/>5.1.1 Limit Case of a Discrete Timed Petri Net 150<br/>5.1.2 Analysis of Some Basic Behaviors 151<br/>5.1.2.1 Sequences of Transitions, Same Maximal Speeds 152<br/>5.1.2.2 Sequences of Transitions, Different Maximal Speeds 156<br/>5.1.2.3 Synchronization 159<br/>5.1.2.4 Timed Continuous Petri Net With a Circuit 160<br/>5.1.2.5 Infinite Maximal Speed 161<br/>5.1.3 Definitions 163<br/>5.1.3.1 Definition and Notation 164<br/>5.1.3.2 Enabling 164<br/>5.1.3.3 Balance 167<br/>5.1.3.4 Evolution Graph 169<br/>5.2 CONFLICTS 170<br/>5.2.1 Existence of an Actual Conflict 170<br/>5.2.2 Conflict Resolution 171<br/>5.3 SPEED CALCULATION ALGORITHMS 173<br/>5.3.1 There is No Structural Conflict 174<br/>5.3.2 Resolution By Priorities 176<br/>5.3.2.1 Expected Results And Problems To Be Solved 176<br/>5.3.2.2 Setting Up the Set of Surely Firable Transitions 180<br/>5.3.2.3 Algorithm And Application 185<br/>5.3.3 Resolution By Sharings And Priorities 189<br/>5.3.3.1 Single Sharing Between Two Transitions 189<br/>5.3.3.2 One or Several Sharings Among Transitions 191<br/>5.3.3.3 Algorithm 197<br/>5.3.4 Complete Algorithm For All IB-states 202<br/>5.4 PROPERTIES 205<br/>5.4.1 Illustratory Examples 205<br/>5.4.1.1 A Simple Production System 205<br/>5.4.1.2 About Marking 0+ 207<br/>5.4.2 General Properties 208<br/>5.4.3 Modeling Power 212<br/>5.5 MAXIMAL SPEEDS FUNCTIONS OF TIME 214<br/>NOTES and REFERENCES 216<br/>Content XVII<br/>6 Timed Hybrid Petri Nets 219<br/>6.1 DEFINITION OF THE MODEL 219<br/>6.1.1 Intuitive Presentation 220<br/>6.1.2 Events To Be Considered 221<br/>6.1.3 Conflict Resolutions 223<br/>6.1.4 Flow Rate and Maximal Firing Speed 226<br/>6.1.5 Formal Definitions 228<br/>6.1.5.1 Definition and Notations 228<br/>6.1.5.2 Enabling in Timed Hybrid Petri Nets 230<br/>6.1.5.3 Evolution Graph 232<br/>6.2 ALGORITHM 235<br/>6.2.1 Resolution for a Case 4 Conflict 236<br/>6.2.1.1 Resolution by Priority 236<br/>6.2.1.2 Resolution by Sharing 238<br/>6.2.1.3 Algorithmic Resolution 240<br/>6.2.2 Consequences of Various Events 241<br/>6.2.3 Timed Hybrid PNs Automatically Treated in Algorithm 6.1 243<br/>6.2.3.1 Hybrid PN Restricted to a Continuous PN 243<br/>6.2.3.2 Consistency of Resolution Rules 245<br/>6.2.4 Algorithm for Building the Evolution Graph 249<br/>6.2.5 Resolution of a Case Not Treated by Algorithm 6.1 254<br/>6.3 VARIANTS OF THE MODEL 255<br/>6.3.1 Synchronized D-Transitions 255<br/>6.3.2 Stochastic Timings for D-Transitions 258<br/>6.3.3 C-Transitions with Flow Rates Functions of Time 259<br/>6.4 EXTENDED TIMED HYBRID PETRI NETS 261<br/>6.4.1 Modeling of Zero Buffers 262<br/>6.4.2 Arc Weight 0+ for Testing if a C-Place is Empty 265<br/>6.4.3 Pure Delay of a Continuous Flow 268<br/>6.4.3.1 Simple Conveyor 268<br/>6.4.3.2 Various Behaviors of a Conveyor 272<br/>6.4.3.3 Fluid Example 274<br/>6.4.4 Conclusion on Timed Extended Hybrid Petri Nets 275<br/>NOTES and REFERENCES 276<br/>7 Hybrid Petri Nets with Speeds Depending on the C-Marking 279<br/>7.1 APPROXIMATION OF TIMED DISCRETE SYSTEMS<br/>BY VHPNs 279<br/>7.1.1 Weakness of Basic Timed Hybrid PNs for Small Numbers 280<br/>7.1.2 Simple Cases of Variable Speed Hybrid PN 281<br/>7.1.3 General Case of VHPN 285<br/>7.1.3.1 Conflicts 285<br/>7.1.3.2 Definition of the Model 287<br/>7.1.3.3 Properties 293<br/>XVIII Content<br/>7.1.4 Application Examples 294<br/>7.1.4.1 Example 1 294<br/>7.1.4.2 Example 2 296<br/>7.2 ASYMPTOTIC HYBRID PETRI NETS (AHPNs) 299<br/>7.2.1 A C-Transition Has a Single Input C-Place 300<br/>7.2.1.1 Constant Feeding Speed of Input C-Place 300<br/>7.2.1.2 Change of Feeding Speed of the Input C-Place 303<br/>7.2.2 Several Input C-Places 305<br/>7.2.3 Generalization 306<br/>7.2.4 Differences Between VHPN and AHPN Behaviors 310<br/>7.3 OTHER MODELS 314<br/>7.3.1 Liquid Flow 314<br/>7.3.2 Differential Hybrid Petri Nets 315<br/>7.3.3 Transfer Line with Operation-Dependent Failures 318<br/>NOTES and REFERENCES 319<br/>Postface 321<br/>Appendices 327<br/>A Regular Expressions and Languages 327<br/>B Conflict Resolution 329<br/>C Elements of Graph Theory 333<br/>D Algebra of Events 335<br/>E About Grafcet 339<br/>F Modeling Power of Synchronized PNs 345<br/>G Timed PNs Are Special Cases of Synchronized PNs 347<br/>H Time Petri Nets 353<br/>I Linearity of the Fundamental Equation for Continuous Petri Nets 357<br/>J Notation 0+ and Non-Standard Analysis 361<br/>K Sharing Between Two Transitions 363<br/>L Graph of Relations Among Conflicts 369<br/>M Piecewise Constant Maximal Speeds 373<br/>N From Hybrid Petri Nets to Hybrid Automata 381<br/>O P&T-Timed Petri Nets and Modeling Power 387<br/>Exercises 393<br/>Solutions to Exercises 433<br/>References 501<br/>Index 515</p>

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