Optimal Petri Net Supervisors of Discrete Event Systems via Weighted and Data Inhibitor Arcs

This paper handles the optimal supervisory control problem of Petri nets (PNs) via two PN structures, namely, weighted and data inhibitor arcs. It is a two-stage method. In the first stage, for each transition that may lead to illegal markings, a set of observer places with weighted inhibitor arcs is used to optimally control the maximal number of marking/transition separation instances (MTSIs) through the proposed integer linear program. Then, the controlled MTSIs are removed from the set of MTSIs. In the second stage, at each iteration, for an MTSI that cannot be controlled at the first control stage, we design an optimal observer place with a data inhibitor arc. This process terminates after all the MTSIs are controlled. The first-stage can sharply lower the computational burden compared with the method by using data inhibitor arcs alone. Finally, a typical example is presented to shed light on this technique. The proposed control strategy can definitely yield an optimal supervisor for any bounded PN on the premise that such a supervisor exists.