Petri-net-based supervisory control for FMSs using the theory of regions

The theory of regions has been recognized as the optimal deadlock prevention policy based on the marking/transition-separation instance (MTSI) or the event-state-separation-problem (ESSP) method for obtaining a maximally permissive controller in existing literature. All legal and live maximal behavior of the Petri nets model can be held by using above methods. However, its major drawback is all MTSIs (ESSPs) are required to indentify for solving the deadlock problems. For the reason, the crucial marking/transition-separation instance (CMTSI) is proposed in this paper to allow designers to deal with system deadlocks using few MTSIs. The advantage of the proposed methodology is that the computational cost can be reduced due to few MTSIs involved in. Importantly, the paper proves and demonstrates that our methodology is utilities.