Concurrency and State Feedbacks in Petri Nets with External Input Places

Abstract

Concurrency is a very important problem in real-time discrete-event systems, and has a crucial effect on control. In this paper, we consider concurrent discrete-event systems modeled by Petri nets with external input places, with a control specification given in terms of a predicate on the set of all reachable markings. First, we derive a simpler condition for the unique existence of the maximally permissive feedback which can be checked without constructing the set of permissive feedbacks. Next, we obtain a necessary and sufficient condition for concurrency to have no effect on the set of permissive feedbacks. And we study the relationship between these two properties. Moreover, we demonstrate synthesis of the unique maximally permissive feedback for a simple manufacturing system.