Study On The Representation And Stability Of Hybrid System Based On Fuzzy Petri Net

Hybrid systems are composed of a continuous part and a discrete part, where thetwo parts have interaction with each other. Such systems have a wide range ofapplications including the computer field and control area. Therefore, the study ofhybrid systems becomes a hot research topic by many scholars. The research ofhybrid systems focuses on how to model the system and the stability of it. Petri net isa main tool for modeling hybrid systems. Through the expansion of the definition ofordinary Petri nets, there are timed Petri nets, hybrid Petri nets which can be used todescribe the differential hybrid systems. However, when the subsystem of the hybridsystem are expressed as fuzzy differential equations, the result is relatively little orbarely not. In order to modeling such a special class of hybrid systems, a new type ofPetri net is presented in this paper and the result of stability is showed as well.The main work of this paper is modeling the fuzzy continuous part of the hybridsystem. Firstly, the current result of hybrid systems is presented and the method ofresearching hybrid systems is studied. Secondly, the paper describes the propositionsof fuzzy differential equations and some basic knowledge of Petri nets with somerelated important class of Petri nets for a brief introduction. Thirdly, based on theordinary Petri nets, a new class of Petri nets, fuzzy differential Petri nets is introduced.For presenting the fuzzy part, this paper introduces a new type of node: fuzzy places(transitions), fuzzy differential places (transitions). Through associating differentialtransitions with firing speed, the fuzzy system's operation characteristics can bepresented. Then analyzes of the hybrid system can be done by the evolution graph offuzzy differential Petri net. Finally, the stability algorithm of the differential fuzzyPetri nets is obtained and the stability of the hybrid system is studied. And an exampleis presented to show how to use the fuzzy differential Petri nets and to show the algorithm of the stability is right.The innovative points of this paper are:1. A new type of Petri nets: fuzzy differential Petri nets, is defined. This paperintroduces new types of Petri net nodes: fuzzy places (transitions), fuzzy differentialplaces (transitions), so the fuzzy differential equations and the interface of the discretepart and the fuzzy continuous part can be presented by the new Petri nets;2. The transition rule of the hybrid system is expanded to hyperplane and suchrules can be modeled by fuzzy differential Petri nets. Because of the expansion, themodeling capabilities of fuzzy differential Petri net are enhanced.3. The stability algorithm of fuzzy differential Petri net is proposed to study thefuzzy differential Petri net and to analysis the performance of the hybrid system.According to the existed stability results of the hybrid system and the properties of thefuzzy differential equations, this paper presents a stability algorithm of fuzzydifferential Petri nets. This algorithm is related to the properties of hybrid systems.