On Computation Reduction of Liveness-Enforcing Supervisors

Abstract

It is well recognized that the computation of an optimal liveness-enforcing supervisor (optimal supervisor for short) for a sequential resource allocation system is intractable due to the nature of the problem itself, since an integer linear programming model has to be formulated to find its solution. In this paper, a novel vector covering approach is developed to reduce the computational cost of designing maximally permissive supervisors for flexible manufacturing systems (FMSs), by reducing the number of operation places and legal markings (LMs) that need to be considered. A vector covering approach is used to find the minimal covered set of first-met bad markings (FBMs). Then, a novel vector covering approach is proposed to reduce the set of LMs to a smaller covering set. The proposed method can reduce the number of both variables and constraints in the integer linear programming problems (ILPPs). It raises the efficiency of designing optimal supervisors by solving ILPPs.