Supervisor Synthesis for Petri Nets With Uncontrollable and Unobservable Transitions

Abstract

This paper focuses on designing event feedback supervisors to enforce control specifications on Petri nets with uncontrollable and unobservable transitions. For each observation, the supervisor is able to select some controllable transitions to disable such that the system never reaches illegal markings. Two different methods are given to design such a supervisor. The first method computes the control policy by solving some integer linear programming problems, while the second one designs supervisors by taking advantage of the structural properties of a class of Petri nets. The computational efficiencies of these two methods increase successively at the expense of their application scopes. Two examples are given to illustrate the proposed methods, respectively. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper consists in ensuring the behavior of a manufacturing system within a given legal behavior. The typical task for a designer is to design a supervisor to restrict that the system never reaches a forbidden state under limited control and observation ability. To this end, this paper proposes two different methods to design such a supervisor. The first one needs to solve integer linear programming problems, while the second one is based on the structural analysis of a special class of systems. It should be noted that although the application scope of the first method is wider, the second method has higher computational efficiency. Therefore, the suitable method can be chosen in accordance with the specific application scenario, which is significant and useful to manufacturing engineers.