Computation of an Optimal Transformed Linear Constraint in a Class of Petri Nets With Uncontrollable Transitions

Deciding how to prevent discrete event systems (DESs) from reaching forbidden states is an important problem in the field of DES supervisory control. For DESs with uncontrollable events, linear constraint transformation becomes a popular technique for solving the forbidden state problem when Petri nets are used as a modeling tool and control specifications are given in the form of linear constraints. This paper proposes a novel linear constraint transformation approach that is applicable to PT-ordinary Petri nets with uncontrollable subnets being forward-concurrent-free. For such nets, a linear constraint can be transformed into an optimal transformed one (i.e., a linear constraint that exactly characterizes the admissible marking set) by using the proposed approach, which is computationally shown to be of polynomial complexity with respect to the net size. An example is presented to illustrate the developed technique.