A Reduced Computation of State Space to Enforce GMECs and Deadlock-Freeness on TPN Systems

This paper analyzes 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. 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, that is derived from another graph recently presented in the literature.