Synthesis of deadlock prevention supervisors using Petri nets

Given an arbitrary Petri net (PN) structure, which may have uncontrollable and unobservable transitions, the deadlock prevention procedure presented here determines a set of linear inequalities on the PN markings. When the PN is supervised so that its markings satisfy these inequalities, the supervised net is proved to be deadlock-free for all initial markings that satisfy the supervision constraints. Deadlock-freedom implies that there will always be at least one transition that is enabled in the closed-loop (supervised) system. The method is not guaranteed to ensure liveness, as it can be applied to systems that cannot be made live under any circumstances. However, for controllable and observable PNs, it is shown that, when the method ensures liveness as well, the liveness-ensuring supervisor is least restrictive. Moreover, it is shown that the method is not restrictive even for PNs in which not all transitions can be made live. The procedure allows automated synthesis of the supervisors.