2023 Volume 59 Issue 12 Pages 550-557
The forbidden state problem is one of control problem for discrete event system as follows: given a Petri net as controlled system and forbidden markings on the net, construct a controller which prevents the system from entering the forbidden markings. Previous studies have proposed methods for obtaining a maximally permissive controller by which the set of reachable markings becomes maximum. However, a control in real systems does not necessarily require a maximally permissive controller and prefers a simple controller with decreasing permissive markings in consideration of control cost and safety. This paper proposes a method for constructing such a controller based on a two-objective integer linear programming problem. The formulated problem increases the computation time drastically. Therefore, the paper considers a reduction of Petri nets by removing redundant transitions to reduce the computation time. The paper also presents the usefulness of the proposed approach by applying to a sequential control system.
