Closed-Loop Deadlock-Free Supervision for GMECs in Time Petri Net Systems

This paper investigates the enforcement of Generalized Mutual Exclusion Constraints (GMECs) and deadlock-freeness on a Time Petri Net (TPN) system with uncontrollable transitions, motivated by the fact that the existing methods enforcing GMECs may degrade the performance of a closed-loop system and lead to deadlock states. A supervisor enforcing a set of GMECs and deadlock-freeness on an underlying untimed Petri net system is assumed to be available. By exploiting timing information and mathematical programming, a control function is designed to restrict the firing intervals of transitions such that a TPN system can avoid entering forbidden states. The key idea behind the proposed approach is the online computation of a graph, called Reduced Modified State Class Graph (RMSCG), that is an extension of the partial modified state class graph recently introduced by the authors. Based on the RMSCG, an online control synthesis procedure is developed, which can enforce the originally given GMECs and deadlock-freeness in a maximally permissive way.