On suboptimal supervisory control of Petri nets in the presence of uncontrollable transitions via monitor places

Recently, a study has been presented for suboptimal supervisory control of Petri nets via monitor (control) places in the presence of uncontrollable transitions. To enforce a generalized mutual exclusion constraint (GMEC) suboptimally on a plant Petri net with uncontrollable transitions, a set of monitor places has been provided to choose from. There are two main results of this study, the first of which is that “there is not an optimal solution to the problem of computing a monitor-based controller to enforce a GMEC on a plant net in the presence of uncontrollable transitions”. The second result deals with the computation of monitor places for the suboptimal supervisory control in such Petri nets. In this paper, it is shown that there may be an optimal solution to the problem of computing a monitor-based controller to enforce a GMEC on a plant net in the presence of uncontrollable transitions. To do this, an example Petri net is considered and then two different optimal (maximally permissive) solutions are provided for this Petri net.