Supervisor Synthesis for a Class of Forbidden State Problems in Discrete Event Systems

A method is proposed to solve a class of forbidden state problems in discrete event systems modeled by Petri nets. They are to enforce a conjunction of generalized mutual exclusion constraints on a controlled Petri net where the influence uncontrollable subnets are joint-free nets. The properties of joint-free nets are proposed. The necessary and sufficient condition of the existence of the maximally permissive (optimal) supervisor is then obtained utilizing these properties. Furthermore, a method is proposed to design the optimal supervisor. The theoretic results are illustrated by an example of synthesizing the optimal supervisor for a manufacturing system.