Supervisory Control for Petri Nets Based on Partial Order Techniques

Supervisory control strategies for discrete event systems based on reachability graphs of Petri nets are in general subject to the state explosion problem. In order to deal with this problem, this paper designs a liveness-enforcing supervisor based on a partial order technique. First, the concept of persistent step graphs is introduced to acquire the partial state information of a system. Based on the persistent step graph analysis, a liveness-enforcing supervisor is obtained by iterately removing the first-met bad markings in the graph. Avoiding the traversal of a system's reachable space, the proposed strategy reduces the computational complexity of reachability graph-based methods, and also achieves the optimal/sub-optimal behavior of the system. Examples are presented to demonstrate the proposed policy.