A Think-Globally-Act-Locally-Based Method of Maximally Permissive Liveness-Enforcing Supervisors for Flexible Manufacturing Systems

With a vector covering (VC) technique, this study proposes a think-globally-actlocally-based (TGAL for short) approach in order to design optimal supervisors for flexible manufacturing systems (FMSs). First, a global idle place is added into a Petri net (PN) model of an FMS according to the TGAL concept. With the global idle place being marked by one token at the initial marking, the model's reachability graph is generated to analyze its liveness. If it is not live, one finds first-met bad markings (FBMs) and all legal markings. By applying the VC approach, these markings can be covered by a minimal covered set (MCdS) of FBMs and a minimal covering set (MCgS) of legal markings, respectively, to remarkably reduce the number of markings under consideration. For each FBM in the MCdS of FBMs, we modify the marking in the MCgS of FBM-related legal markings to guarantee that every place has the maximal tokens. By using the modified FBM-related legal markings, a set of optimal control places (monitors) can be calculated by solving an integer linear programming problem. Necessary monitors are figured out by a redundancy test. Then, we increase the number of tokens in the global idle place. This process is repeated until all legal markings are reachable. Then, a maximally permissive supervisor can be obtained. Finally, by means of experimental studies, the proposed method is tested for some PN models, showing that the designed supervisors are maximally permissive since the monitors do not prohibit any legal markings.