Control Strategy of Discrete Event Systems Modeled by Labeled Petri Nets Based on Transition Priority

This paper deals with the supervisory control problem of discrete event systems modeled with labeled Petri nets. A transition priority matrix is proposed to control the firing of controllable transitions to prevent the system from entering illegal states. First, given a labeled Petri net system, an integer linear programming problem based on the pre-defined generalized mutual exclusion constraints and deadlocks is built to find out weakly illegal markings in its basis reachability graph. This approach is efficient since the exhaustive enumeration of the reachability space can be avoided. Second, since the firing of an uncontrollable transition sequence at a weakly illegal marking leading to an illegal state is inevitable, our goal is to prevent the system from entering weakly illegal states. A control algorithm is proposed to find a feasible transition priority matrix to avoid weakly illegal markings by controlling the firings of observable transitions. The dynamic transition priority matrix changes according to the current state of the system. Finally, two cases are studied to verify the control strategy. This control strategy does not complicate the structure of a system and can effectively avoid state-space explosion.