The Relationship Of Supervisory Control Theory Between Crisp And Fuzzy Discrete Event Systems

In this paper,firstly,we discuss the relationship of event feedback control between crisp discrete event systems and fuzzy discrete event systems.The relationship of nor-mality between a fuzzy language and its corresponding strong cut sets languages is studied.We define a fuzzy supervisor of composition of two fuzzy automata,and the relationship between the controllability of fuzzy language and the controllability of its corresponding strong cut sets languages in the composed system is studied.Then the existence theorem of a fuzzy supervisor in the composed system is obtained.Next,the relationship of reliable decentralized supervisory control between crisp and fuzzy discrete event systems is discussed on the basis of their own theories.For a given fuzzy specification language,if it's reliably({Pi}i?I,Ec,k)-co-observable,then its corresponding strong cut sets languages are reliably({Pi}i?I,Ec,k)-co-observable.And the relationship of({Pi}i?I,k)-normality between a fuzzy language and its cor-responding strong cut sets languages is studied.Furthermore,by the existence of a k-reliable fuzzy decentralized supervisory of a given fuzzy language,the existence of a k-reliable decentralized supervisory of its corresponding strong cut sets languages is obtained.Finally,the relationship of state feedback control between crisp and fuzzy discrete event systems is studied.By combining the theory of fuzzy sets with the definition of predicates,we define a fuzzy predicate and fuzzy predicate transformations in fuzzy discrete event systems.On this basis,Euc-invariance and control invariance of fuzzy predicates are redefined.If the given fuzzy predicate is Euc—invariant,then the corre-sponding strong cut sets predicates are Euc-invariant.