This paper focuses on enforcing disjunctive generalised mutual exclusion constraints, referred to as OR-GMEC, on Petri net models. In this case, the legal marking set is non-convex, while the admissible marking set can either be convex or non-convex. The study presents a necessary condition for the existence of a monitor-based solution for a non-convex admissible marking set. Subsequently, the disjunctive constraints are developed to derive an optimal supervisory controller, and an algorithm is proposed for solution computation. The design procedure includes off-line computation mechanisms, yielding an optimal (maximally permissive) supervisor with only a few monitors. The key advantage of the suggested approach is that, unlike the current techniques, the number of monitors in the supervisor’s structure does not rise as the number of constraints increases.
Read full abstract