Design of supervisors for linear marking specifications in labeled Petri nets

In this paper we study the problem of enforcing a generalized mutual exclusion constraint (GMEC) in a labeled Petri net that contains indistinguishable transitions by a monitor-based supervisor. We show that a monitor-based supervisor can be designed based on the influence of events if the GMEC is deterministic. On the other hand, for a nondeterministic GMEC, we introduce the notion of dependency of transitions, which provides a quantitative relation between the transition firings and the occurrence of dependent events. Based on the dependency of transitions, we propose a structural approach to compute a monitor function using Hilbert basis, which helps us develop an algorithm to design an online supervisor using the monitor function. Our approach has low online computational load since marking estimation is avoided.