抄録
We consider the controlled discrete event system formulated by Golaszewski and Ramadge, which is a generalization of Ramadge and Wonham's model, and specifications are assumed to be described by predicates on the state set. A predicate P is said to be control-invariant iff there exists a state feedback by which the controlled process remains in a set of states satisfying P. Such a feedback is called a control-alternative. In general, there are more than one control-alternatives for a control-invariant predicate, and the maximal and minimal elements in the set of control-alternatives, which is called maximally and minimally permissive feedbacks respectively, do not always exist uniquely.
This paper proves the necessary and sufficient conditions for the unique existence of maximally and minimally permissive feedbacks by introducing concepts of weak interaction and weak closedness. Since all the reachable states in a controlled system satisfy the given predicate if the initial state does, we introduce maximally and minimally permissive practical feedbacks, and discuss their unique existence. Finally, we deal with the case that the set of control patterns is a lattice, and several properties are shown.
