Structure Description And Formal Analysis Of Petri Net Systems

Petri nets are a modeling and analyzing tool of nets. It has many unique advantages such aspowerful simulation ability, step-by-step description ability and analyzing ability. It could beexpressed by graph directly; it also has the profound background foundation of mathematics andcan represent dynamic performance of systems. Thus it is widely used in many fields. Timed Petrinets are able to make every transition correspond to time function. It enhances the simulation abilityof Petri nets and has been widely used in discrete event system. Fuzzy Petri net is an importantbranch and can be effectively dealt with imprecise, uncertain and complex factors of the systemmodel problem. Through the network model of the actual system analysis, can be revealed realisticsystem and behavioral important information that can be used to estimate the actual systembehavior and analysis.First of all, the state of art of Petri nets is reviewed, concerning the current theory andapplications of Petri nets, and as well the research purpose and significance of studying Petri nets isdescribed. Secondly, according to different application background, for all current model ofreasoning Fuzzy Petri nets, the four kinds of typical fuzzy reasoning methods are compared in detailin this paper. The results show that the existing Fuzzy Petri nets have its own characteristics anddeficiencies in modeling and analyzing the circulation of economic system and ecological system.Based on the definition of fuzzy dynamic Petri nets and its operation rules, this paper studies aFuzzy Petri nets system with deadlock and traps structure and presents the performance analysis ofthe fuzzy Petri nets. A Fuzzy Petri net with different initial markings is given as an example toillustrate its dynamic performance behavior. Again, Based on a class of timed discrete Petri netswhich have self-loop, an equivalent and novel timed discrete Petri Net is first presented , and theauthor gives its dynamic rules, including firing rules, first in first out rule, firing quantity formula aswell as some related important conclusions. Formal analysis concerning it and computationalgorithm are obtained.This equivalence helps to reduce the dimension of the marking vector significantly. At thesame time, two examples are given to reveal the change of tokens in different states at differenttimes and draw the corresponding curve to verify the correctness and rationality of this formalanalysis.In this paper, closed-loop Fuzzy Petri nets with deadlock and trap can be more effectivelyused to model and analyze economic system, ecological system, especially for further expansion inthe application field of Fuzzy Petri net. It plays an important role in the development of the Fuzzy Petri net theory; especially it is very important to further study on the structure of the closed-loopFuzzy Petri net theory and application. In addition, the paper also proposed a formal analysismethod of a class of timed discrete Petri nets. It contributes to study the structure nature of timeddiscrete Petri nets in order to avoid system deadlock and has important applications in the practicalmodeling process.Finally, a comprehensive summary to the thesis is given and the drawbacks and futureresearch directions are pointed out.