On closed-loop liveness of discrete event systems under maximally permissive control

A class of controlled discrete-event systems that can be modeled as cyclic controlled marked graphs (CMGs), a special case of control Petri nets, is considered. Liveness of the controlled system under the maximally permissive feedback control is examined. In the CMG context, closed-loop liveness implies that from any reachable marking (state), any transition can be enabled to fire. The concept of synchronic distances in Petri nets is used to prove sufficient conditions under which the maximally permissive control results in a live closed-loop system.<>