On Closed-Loop Liveness of Discrete-Event Systems Under Maximally Permissive Control

We consider a class of controlled discrete-event systems modeled as controlled marked graphs (CMG’s), a special case of controlled Petri nets. In a previous paper a computationally efficient method was presented for solving a class of forbidden state problems in CMG’s. In this note we consider liveness of the controlled system under the maximally permissive feedback control policies. In the CMG context, closed-loop liveness implies that from any reachable marking (state) any transition can be enabled to fire. Using the concept of synchronic distances in Petri nets, we prove sufficient conditions under which the maximally permissive control results in a live closed-loop system.