Identification of controllable transitions to decide the existence of an optimal liveness-enforcing supervisor for a class of Petri nets

Behaviour permissiveness is an important criterion in evaluating the performance of a liveness-enforcing supervisor for discrete event systems. The existence of uncontrollable events is a standard feature in the supervisory control of discrete event systems. A natural problem arising in this area is the existence of an optimal supervisor when there exist uncontrollable events in a plant. For a class of Petri net models of flexible manufacturing systems, whose optimal liveness-enforcing Petri net supervisors can be synthesized by a particular method through the addition of a set of monitors, this paper aims to identify a set of transitions such that the existence of an optimal liveness-enforcing net supervisor depends on their controllability. The controllability of a transition is decided by solving a linear programming problem to verify whether a monitor with arcs to the transition can act to inhibit it when it is otherwise enabled. A number of examples are presented to demonstrate the application of the proposed methods.