^|^Gamma;-Controllability and State Feedbacks in Discrete Event Systems
Shigemasa Takai, Toshimitsu Ushio, Shinzo Kodama · Transactions of the Society of Instrument and Control Engineers · 1995
In this paper, we consider state feedback control of discrete event systems, where we assume that the set of control patterns is closed under union. A control specification is assumed to be given in terms of a predicate on the set of states. First, we introduce the notion of Γ-controllability of predicates. We then show that Γ-controllability is a necessary and sufficient condition for the existence of a state feedback controller which achieves the control specification. However, the given predicate is not necessarily Γ-controllable. In such a case, its supremal Γ-controllable subpredicate plays an important role in synthesizing state feedback controllers. So we present a necessary and sufficient condition for the existence of a Γ-controllable subpredicate, and derive a closed form expression of the supremal Γ-Controllable subpreicate when the set of states satisfying the given predicate is finite.