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

A class of controlled discrete-event systems modeled as controlled marked graphs (CMGs), a special case of controlled Petri nets, is considered. Liveness of controlled systems under maximally permissive feedback control policies is investigated. 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.<>