Live and maximally permissive controller synthesis using the theory of regions
Résumé
This paper addresses the forbidden state problem of Petri nets with liveness requirement and uncontrollable transitions. The proposed approach synthesizes in two steps an optimal Petri net-based controller, whenever such a controller exists. First, the behavior of the closed loop system is computed with a Ramadge-Wonham-like approach. Then, control places, that realize the computed behavior when added to the original model, are synthesized. Necessary and sufficient condition of the existence of such places is obtained. A manufacturing application of the method shows its efficiency.