Maximally Permissive Supervisor Synthesis Using Reachability and Structural Analysis of Petri Nets

Abstract

To find a set of linear constraints for maximally permissive supervisory control of an automated manufacturing system, in the existing work, a mixed integer linear programming (ILP) problem is generally formulated and solved for some particular markings based on reachability analysis, which is computationally inefficient due to the combinatorial nature of an ILP problem. This paper addresses the deadlock prevention problem by developing efficient methods to reduce the computational overhead through the establishment of algebraic conditions to verify the maximal permissiveness of linear constraints imposed on the studied systems. By taking the advantage of structural properties of Petri nets under consideration, we identify some taxonomies of illegal markings that can be optimally prohibited. A linear programming method is developed to deal with those markings that cannot be processed by the proposed structural analysis. It is shown that for the considered class of Petri nets, no mixed ILP problem needs to solve and the computational burden is dramatically reduced. Two examples are employed to demonstrate the efficiency of the developed method.