Supervisor synthesis for discrete event systems with arbitrary forbidden state specifications

In this paper, we consider the forbidden state problem in discrete event systems modeled by Petri nets with uncontrollable and/or unobservable transitions. To handle the interleaving of uncontrollable and unobservable transitions, we first use the reverse net to compute a set of weakly forbidden markings (i.e., a set of markings from which forbidden markings can be reached by firing uncontrollable transitions). We then use basis markings to represent the set of consistent markings for Petri nets with acyclic unobservable subnets (or unobservable subnets with certain cycles). We determine the control policy by checking if a possible subsequent basis marking belongs to the set of weakly forbidden markings; if so, we disable the corresponding (controllable) transition. The setting in this paper generalizes previous work by allowing partial observation, partial control, and a finite number of arbitrary forbidden states.