State Feedback Control Of Partially Observable Fuzzy Discrete Event Systems

In this paper,we extend the partially observable crisp discrete event systems to partially observable fuzzy discrete event systems,and discuss the state feedback control of partially observable fuzzy discrete event systems.Firstly,to get the model of the partially observable fuzzy discrete event systems,we introduce output mapping and output symbol set into the partially observable fuzzy discrete event systems.We define reachable fuzzy controllers and fuzzy state allowable feedback controllers.On this basis,we discuss the optimal state allowable feedback control and optimal h-state allowable feedback control of partially observable fuzzy discrete event systems.We define the observability of fuzzy predicates and give the necessary and sufficient conditions for the observability of fuzzy predicates.Secondly,for a specified target fuzzy predicate,it is proved that there is a reasonable fuzzy controller to make the reachable fuzzy predicate of the closed-loop system equal to the specified target fuzzy predicate if and if only the fuzzy predicate is controllable and observable.When the fuzzy predicate is uncontrollable or unobservable,we can find the maximum controllable observable fuzzy sub-predicate of the fuzzy predicate,then we study the state feedback control of partially observable fuzzy discrete event systems by the maximum controllable observable fuzzy sub-predicate.Finally,for some fuzzy predicate of the especial partially observable fuzzy discrete event system,we construct a corresponding fully observable fuzzy discrete event system.On this basis,we discuss the relationship between the invariance and controllability of fuzzy predicates.