On the enforcement of a class of nonlinear constraints on Petri nets

This paper deals with the enforcement of nonlinear constraints on Petri nets. A supervisory structure is proposed for a class of nonlinear constraints. In order to enforce a nonlinear constraint on a Petri net, we propose a transition transformation technique to replace a transition in an original net by a set of transitions. Then, a control place is designed to control the firing of these transitions, aiming to enforce the nonlinear constraint. The proposed supervisor is maximally permissive in the sense that it can make all markings in the admissible-zone reachable and all markings in the forbidden-zone unreachable. The proposed method is applicable to bounded Petri nets. Finally, a number of examples are provided to demonstrate the proposed approach.