Synthesis of Petri net supervisors for FMS via redundant constraint elimination

The Minimal number of Control Places Problem (MCPP), which is formulated to obtain optimal and structurally minimal supervisors, needs extensive computation. The current methods to reduce the computational burden have mainly focused on revision of the original formulation of MCPP. Instead, this paper presents methods to accelerate its solution by eliminating its redundant reachability constraints. The optimization problem scale required for supervisor synthesis is thus drastically reduced. First, a sufficient and necessary condition for a reachability constraint to be redundant is established in the form of an integer linear program (ILP), based on a newly proposed concept called feasible region of supervisors. Then, two kinds of redundancy elimination methods are proposed: an ILP one and a non-ILP one. Most of the redundant reachability constraints can be eliminated by our methods in a short time. The computational time to solve MCPP is greatly reduced after the elimination, especially for large-scale systems. The obtained supervisors are still optimal and structurally minimal. Finally, numerical tests are conducted to show the efficiency and effectiveness of the proposed methods.