CHARACTERIZATION OF ALL M-CONTROLLABLE SUBPREDICATES OF A GIVEN PREDICATE

This paper studies state feedback control of discrete event systems un der partial observation. A control specification is assumed to be spec ified by a predicate on the state space. It has been proved that M-con trollability is a necessary and sufficient condition for the existence of a state feedback controller which solves the control problem. Howe ver, the given predicate is not necessarily M-controllable. In this ca se, a state feedback controller is synthesized for its M-controllable subpredicate. This paper characterizes all M-controllable subpredicate s of a given predicate. Using the characterization, an M-controllable subpredicate that is larger than the supremal strongly M-controllable subpredicate is obtained. So the obtained M-controllable subpredicate is a better approximation of the given predicate.