Most permissive Petri net supervisors for flexible manufacturing systems
Résumé
This paper presents a deadlock prevention approach to find a maximally permissive liveness-enforcing pure
Petri net supervisor, expressed by a set of monitors, for a flexible manufacturing system (FMS), if such a
supervisor exists. Otherwise, it derives the most permissive one in the sense that there are no other Petri net
supervisors that are more permissive than it. The proposed approach computes the reachability graph of a
plant model only once. By using a vector covering approach, the sets of legal markings and first-met bad
markings (FBMs) are reduced to two smaller ones, namely the minimal covering set of legal markings and the
minimal covered set of FBMs. At each iteration, an FBM is selected. By solving an integer linear
programming problem (ILPP), a place invariant (PI) is designed to prevent the FBM from being reached while
no marking in the minimal covering set of legal markings is forbidden. If the ILPP has no solution, implying
that there is no maximally permissive Petri net supervisor for the plant net model, another ILPP is designed to
remove the least number of legal markings whose reachability conditions contradict others. Then, a PI is
redesigned to ensure that the remaining legal markings are reachable. This process is carried out until no FBM
can be reached. Finally, a most permissive liveness-enforcing supervisor is obtained. FMS examples are
presented to illustrate the proposed approaches.