抄録
Petri nets with external input places are useful tools for analysing control problems of discrete-event systems. If control synthesis problems can be represented by control-invariant predicates on the reachable set, then there exist control-alternatives, which are static state-feedbacks for the control problems. In this paper, the maximal control-alternative is called the maximally permissive feedback, which does not always exist uniquely.
This paper shows that the weak interaction of the predicate is the necessary and sufficient condition for the uniqueness of the maximally permissive feedback. And modular feedback is considered in the case that control synthesis problems are represented by conjunction and/or disjunction of predicates. Specially, it is shown that the maximally permissive feedback for conjunction of predicates is equal to the modular one at markings satisfying the conjunction if each predicate is weakly interactive.
