Discrete, Continuous, and Hybrid Petri Nets

Cover......Page p0001.djvu
Discrete, Continuous, and Hybrid Petri Nets (Second edition)......Page p0004.djvu
9783642061295......Page p0005.djvu
Foreword......Page p0006.djvu
Preface......Page p0010.djvu
Contents......Page p0014.djvu
Notation......Page p0020.djvu
1.1.1 Places, Transitions, and Arcs......Page p0024.djvu
1.1.2 Marking......Page p0025.djvu
1.1.3 Firing of a Transition......Page p0026.djvu
1.1.4 Autonomous and Non-Autonomous Petri Nets......Page p0027.djvu
1.2 SPECIAL PETRI NETS......Page p0028.djvu
1.2.1 Particular Structures......Page p0029.djvu
1.2.1.2 Event Graph......Page p0030.djvu
1.2.1.5 Simple Petri Net......Page p0031.djvu
1.2.2.1 Generalized Petri Nets......Page p0032.djvu
1.2.2.2 Finite Capacity Petri Nets......Page p0034.djvu
1.2.2.3 Colored Petri Nets......Page p0035.djvu
1.2.2.4 Extended Petri Nets......Page p0036.djvu
1.2.2.5 Priority Petri Nets......Page p0038.djvu
1.2.2.6 Non-Autonomous Petri Nets......Page p0039.djvu
1.3 MODELING OF SOME CONCEPTS......Page p0040.djvu
NOTES and REFERENCES......Page p0043.djvu
2.1.1 Notations and Definitions......Page p0044.djvu
2.1.2 Bounded Petri Net, Safe Petri Net......Page p0047.djvu
2.1.3 Liveness and Deadlock......Page p0048.djvu
2.1.4.2 Concurrency and Multiple Firing......Page p0053.djvu
2.1.4.4 Enabling Degree and General Conflict......Page p0055.djvu
2.1.5.1 Conservative Component......Page p0057.djvu
2.1.5.2 Repetitive Component......Page p0058.djvu
2.2 SEEKING THE PROPERTIES OF PETRI NETS......Page p0060.djvu
2.2.1.1 Graph of Markings......Page p0061.djvu
2.2.1.2 Coverability Root Tree......Page p0062.djvu
2.2.2.1 Notations and Definitions......Page p0065.djvu
2.2.2.2 Fundamental Equation......Page p0067.djvu
2.2.2.3 Conservative Components & Marking Invariants......Page p0069.djvu
2.2.2.4 Repetitive Components & Firing Invariants......Page p0072.djvu
2.2.2.5 Seeking P-invariants and T-invariants......Page p0073.djvu
2.2.3 Reduction Methods Preserving Some Properties......Page p0075.djvu
2.2.4.1 Strongly Connected Event Graphs......Page p0076.djvu
2.2.4.2 Siphons and Traps......Page p0077.djvu
2.2.4.3 Liveness Related to Other Properties......Page p0079.djvu
2.2.5.1 Structuring......Page p0080.djvu
NOTES and REFERENCES......Page p0082.djvu
3.1 INTRODUCTION......Page p0084.djvu
3.2 SYNCHRONIZED PETRI NETS......Page p0086.djvu
3.2.1.1 Basic Behaviors and Concepts......Page p0087.djvu
3.2.1.2 Illustrative Examples......Page p0090.djvu
3.2.1.3 Simultaneous Events......Page p0092.djvu
3.2.2.1 Elementary Firing Sequence......Page p0093.djvu
3.2.2.2 Iterated Firing......Page p0096.djvu
3.2.2.3 Coverability root tree of the stable reachable markings......Page p0098.djvu
3.2.3.1 Promptness or Stability......Page p0102.djvu
3.2.3.2 Boundedness, Safeness, Liveness, Deadlock-Freeness......Page p0105.djvu
3.2.3.3 Environment......Page p0109.djvu
3.3 INTERPRETED PETRI NETS......Page p0111.djvu
3.3.1 Definition of a Control Interpreted Petri Net......Page p0112.djvu
3.3.2 Interpretation Algorithm of a Control Interpreted..PN......Page p0116.djvu
3.3.3 Interpreted PN Without Outputs: Generalization of the Concept of Synchronized PN......Page p0119.djvu
3.4.1 General Information......Page p0121.djvu
3.4.2.1 P-Timed Petri Nets......Page p0124.djvu
3.4.2.2 T-Timed Petri Nets......Page p0126.djvu
3.4.2.3 Stationary Behavior......Page p0130.djvu
3.4.3.1 Basic Model......Page p0132.djvu
3.4.3.2 Generalized Stochastic Petri Net......Page p0135.djvu
3.4.3.3 Analysis and Simulation of Stochastic PNs......Page p0136.djvu
NOTES and REFERENCES......Page p0137.djvu
4.1 MOTIVATION......Page p0140.djvu
4.2.1 From Discrete Petri Net To Continuous Petri Net......Page p0142.djvu
4.2.2 Definition......Page p0144.djvu
4.2.3 Reachability and Conflicts......Page p0146.djvu
4.2.3.1 Reachability Graph......Page p0147.djvu
4.2.3.2 Firing Sequence and Reachability Space......Page p0149.djvu
4.2.3.3 Conflicts......Page p0151.djvu
4.2.4 Comments about units......Page p0152.djvu
4.3 AUTONOMOUS HYBRID PETRI NETS......Page p0153.djvu
4.3.1 Intuitive presentation......Page p0154.djvu
4.3.2 Definition......Page p0157.djvu
4.3.3.1 Reachability Graph......Page p0160.djvu
4.3.3.2 Firing Sequence and Reachability Space......Page p0164.djvu
4.3.3.3 Conflicts......Page p0165.djvu
4.4.1.1 Definitions......Page p0166.djvu
4.4.1.2 Properties......Page p0167.djvu
4.4.2 Reachability and Limit Reachability for a Continuous PNs......Page p0168.djvu
4.4.3 ε-Liveness for a Continuous Petri Net......Page p0171.djvu
4.4.4 Lim-Liveness for a Continuous Petri Net......Page p0172.djvu
4.4.5.2 Reachability and Liveness......Page p0174.djvu
4.4.5.3 Incidence Matrix......Page p0175.djvu
4.5.1 Threshold Test......Page p0176.djvu
4.5.2 Zero Test and Arc Weight 0^+......Page p0177.djvu
4.5.3 Marking 0^+......Page p0179.djvu
4.5.4 Definition......Page p0180.djvu
NOTES and REFERENCES......Page p0181.djvu
5.1 DEFINITION OF THE MODEL......Page p0182.djvu
5.1.1 Limit Case of a Discrete Timed Petri Net......Page p0183.djvu
5.1.2 Analysis of Some Basic Behaviors......Page p0184.djvu
5.1.2.1 Sequences of Transitions, Same Maximal Speeds......Page p0185.djvu
5.1.2.2 Sequences of Transitions, Different Maximal Speeds......Page p0189.djvu
5.1.2.3 Synchronization......Page p0192.djvu
5.1.2.4 Timed Continuous Petri Net With a Circuit......Page p0193.djvu
5.1.2.5 Infinite Maximal Speed......Page p0195.djvu
5.1.3.1 Definition and Notation......Page p0197.djvu
5.1.3.2 Enabling......Page p0198.djvu
5.1.3.3 Balance......Page p0200.djvu
5.1.3.4 Evolution Graph......Page p0202.djvu
5.2.1 Existence of an Actual Conflict......Page p0203.djvu
5.2.2 Conflict Resolution......Page p0205.djvu
5.3 SPEED CALCULATION ALGORITHMS......Page p0207.djvu
5.3.1 There is No Structural Conflict......Page p0208.djvu
5.3.2.1 Expected Results And Problems To Be Solved......Page p0210.djvu
5.3.2.2 Setting Up the Set of Surely Firable Transitions......Page p0214.djvu
5.3.2.3 Algorithm And Application......Page p0218.djvu
5.3.3.1 Single Sharing Between Two Transitions......Page p0223.djvu
5.3.3.2 One or Several Sharings Among Transitions......Page p0226.djvu
5.3.3.3 Algorithm......Page p0231.djvu
5.3.4 Complete Algorithm For All IB-states......Page p0236.djvu
5.4.1.1 A Simple Production System......Page p0239.djvu
5.4.1.2 About Marking 0^+......Page p0241.djvu
5.4.2 General Properties......Page p0243.djvu
5.4.3 Modeling Power......Page p0246.djvu
5.5 MAXIMAL SPEEDS FUNCTIONS OF TIME......Page p0248.djvu
NOTES and REFERENCES......Page p0250.djvu
6.1 DEFINITION OF THE MODEL......Page p0254.djvu
6.1.1 Flow Rate and Maximal Firing Speed......Page p0255.djvu
6.1.2 Illustrative Example......Page p0258.djvu
6.1.3 Events To Be Considered......Page p0260.djvu
6.1.4 Conflict Resolutions......Page p0261.djvu
6.1.5.1 Definition and Notations......Page p0264.djvu
6.1.5.2 Enabling in Timed Hybrid Petri Nets......Page p0266.djvu
6.1.5.3 Evolution Graph......Page p0269.djvu
6.2 ALGORITHM......Page p0271.djvu
6.2.1.1 Resolution by Priority......Page p0272.djvu
6.2.1.2 Resolution by Sharing......Page p0274.djvu
6.2.1.3 Algorithmic Resolution......Page p0276.djvu
6.2.2 Consequences of Various Events......Page p0277.djvu
6.2.3.1 Hybrid PN Restricted to a Continuous PN......Page p0279.djvu
6.2.3.2 Consistency of Resolution Rules......Page p0281.djvu
6.2.4 Algorithm for Building the Evolution Graph......Page p0285.djvu
6.2.5 Resolution of a Case Not Treated by Algorithm 6.1......Page p0291.djvu
6.3 VARIANTS OF THE MODEL......Page p0292.djvu
6.3.1 Synchronized D-Transitions......Page p0293.djvu
6.3.2 Stochastic Timings for D-Transitions......Page p0296.djvu
6.3.3 Hybrid Petri Nets with Time Transitions......Page p0297.djvu
6.3.4 C-Transitions with Flow Rates Functions of Time......Page p0298.djvu
6.3.5 Colored Hybrid Petri Net......Page p0300.djvu
6.4 EXTENDED TIMED HYBRID PETRI NETS......Page p0301.djvu
6.4.1 Modeling of Zero Buffers......Page p0302.djvu
6.4.2 Arc Weight 0^+ for Testing if a C-Place is Empty......Page p0305.djvu
6.4.3.1 Simple Conveyor......Page p0308.djvu
6.4.3.2 Various Behaviors of a Conveyor......Page p0311.djvu
6.4.3.3 Fluid Example......Page p0314.djvu
6.4.4 Conclusion on Timed Extended Hybrid Petri Nets......Page p0315.djvu
NOTES and REFERENCES......Page p0316.djvu
7 Hybrid Petri Nets with Speeds Depending on the C-Marking......Page p0318.djvu
7.2.1.1 Constant Feeding Speed of Input C-Place......Page p0339.djvu
7.2.1.2 Change of Feeding Speed of the Input C-Place......Page p0342.djvu
7.2.2 Several Input C-Places......Page p0344.djvu
7.2.3 Generalization......Page p0346.djvu
7.2.4 Differences Between VHPN and AHPN Behaviors......Page p0349.djvu
7.3.1 Liquid Flow......Page p0353.djvu
7.3.2 Differential Hybrid Petri Nets......Page p0354.djvu
7.3.3 Transfer Line with Operation-Dependent Failures......Page p0358.djvu
NOTES and REFERENCES......Page p0359.djvu
Postface......Page p0362.djvu
A - Regular Expressions and Languages......Page p0368.djvu
B - Conflict Resolution......Page p0370.djvu
C - Elements of Graph Theory......Page p0374.djvu
D - Algebra of Events......Page p0376.djvu
E - About Grafcet......Page p0380.djvu
F - Modeling Power of Synchronized Petri Nets......Page p0386.djvu
G - Timed PNs Are Special Cases of Synchronized Petri Nets......Page p0388.djvu
H - Time Petri Nets......Page p0394.djvu
I - Linearity of the Fundamental Equation for Continuous Petri Nets......Page p0398.djvu
J - Notation 0^+ and Non-Standard Analysis......Page p0402.djvu
K - Sharing Between Two Transitions......Page p0404.djvu
L - Graph of Relations Among Conflicts......Page p0410.djvu
M - Piecewise Constant Maximal Speeds......Page p0414.djvu
N - From Hybrid Petri Nets to Hybrid Automata......Page p0422.djvu
O - P&T-Timed Petri Nets and Modeling Power......Page p0428.djvu
Exercises......Page p0434.djvu
Solutions to Exercises......Page p0476.djvu
References......Page p0548.djvu
Index......Page p0564.djvu