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Optimal Supervisory Control of Flexible Manufacturing Systems by Petri Nets: A Set Classification Approach
              Supervisory control is usually considered as an external control mechanism to a system by controlling the occurrences of its controllable events. There exist Petri net models whose legal reachability spaces are nonconvex. In this case, they cannot be optimally controlled by the conjunctions of linear constraints. For Petri net models of flexible manufacturing systems, this work proposes a method to classify the legal markings into several subsets. Each subset is associated with a linear constraint that can forbid
all first-met bad markings. Then, the disjunctions of the obtained constraints can make all legal markings reachable and forbid all first-met bad markings, i.e., the controlled net is live andmaximally
permissive. An integer linear programming model is formulated to minimize the number of the constraints. A supervisory structure is also proposed to implement the disjunctions of the constraints. Finally,
examples are provided to illustrate the proposed method. Note to Practitioners—The resolution of deadlocks in flexible manufacturing systems (FMSs) is an important issue since they may lead to catastrophic results in highly automated production systems. Based on Petri nets, a deadlock prevention approach always aims to design a controller to ensure that deadlocks never occur. Behavioral permissiveness is an important criterion in evaluating the performance of a supervisor. A maximally permissive supervisor can generally lead to high utilization of resources and productivity of a system. However, if the legal reachability space of a net model is nonconvex, it cannot be optimally controlled by
the conjunctions of linear constraints. In this case, this research develops maximally permissive supervisory control by enforcing disjunctive constraints whose number is minimized. The proposed
method is applicable to all FMS-oriented Petri net models proposed in the literature. Index Terms—Deadlock prevention, first-met bad marking (FBM), flexible manufacturing system (FMS), maximal permissiveness, Petri net, supervisory control.            
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