Optimal Petri net supervisor with lowest implemental cost for flexible manufacturing systems

This paper develops a place invariant based deadlock prevention method to obtain an optimal Petri net supervisor by considering its implemental cost. A supervisor is expressed by control places and the arcs connecting control places to transitions. We assign an implemental cost for each control place and arc. Maximally permissiveness can be achieved by designing place invariants that make all legal markings reachable while all first-met bad marking unreachable. By solving an integer linear programming problem (ILPP), a set of optimal control places are obtained and the objective function is used to minimize the implemental cost of the final supervisor. A vector covering approach is used to reduce the number of constraints and variables in the ILPP, aiming to reduce the computational overhead of the proposed method. Finally, a number of examples are used to illustrate the proposed approach.