State-feedback Control Of Fuzzy Discrete Event Systems

The control theory of fuzzy discrete event systems has been widely applied in the control system with discrete characteristics,especially in the medical field.It has been successfully applied in the treatment of diabetes,HIV and other diseases.In this paper,we define the partial order of fuzzy predicates and the fuzzy weakest precondition and the fuzzy strongest postcondition of fuzzy discrete event systems,and it is proved that the result of first making the fuzzy weakest precondition transformation and then making the fuzzy strongest postcondition transformation for a given fuzzy predicate in the fuzzy discrete event systems is equal to the original given predicate;The result of first making the fuzzy strongest postcondition transformation and then making the fuzzy weakest precondition transformation for a given fuzzy predicate in the fuzzy discrete event systems is greater than the original given predicate;The definition of the fuzzy weakest free precondition is given,and it is proved that the fuzzy weakest free precondition of the conjunction(disjunction)of fuzzy predicates is equal to the conjunction(disjunction)of the fuzzy weakest free preconditions of the fuzzy predicates.Secondly,we define the fuzzy state feedback controller in the fuzzy discrete event systems.The control invariance and ?_u-invariance of the fuzzy predicates are defined.It is proved that the control invariance and ?_u-invariance of the fuzzy predicates are equivalent.There must be the largest fuzzy state feedback controller when the predicate is control invariable.Finally,the definition of controllable fuzzy predicate is given,and it is proved that there is a fuzzy state feedback controller to make the reachable fuzzy predicate of closed-loop system equal to the given fuzzy predicate if and only if the fuzzy predicate is controllable.We define the controllable fuzzy subpredicate and give the method of calculating the maximum controllable fuzzy subpredicate.