Automated Synthesis of Liveness Enforcing Supervisors Using Petri Nets

Given an arbitrary Petri net structure, which may have uncontrollable and unobservable transitions, the liveness enforcement procedure presented here determines a set of linear inequalities on the marking of a Petri net. When the Petri net is supervised so that its markings satisfy these inequalities, the supervised net is proved to be live for all initial markings that satisfy the supervision constraints. Also the supervision is proved to be maximally permissive for a large class of Petri nets, which includes the fully controllable and observable Petri nets. Moreover, the supervisor supports specifications requiring only some of the Petri net transitions to be live. The maximal permissivity typically applies also for this case. The procedure allows automated synthesis of the supervisors. The sufficient conditions for which our theoretical results are guaranteed to apply can be automatically verified.