Supervisor synthesis of Petri net with uncontrollable transitions

In supervisory synthesis of discrete event system (DES) modeled by Petri nets with uncontrollable events, when the specifications are Parikh vector constraints, a method is proposed to transform illegal constraint into admissible constraint by using transformation matrix R. Matrix equation is constructed to obtain R, and the existence of R can be predicted by the compatibility of the matrix equation in advance. Generalized inverse matrix is applied to achieve the solution of R, as well as the admissible constraint and supervisor. The principle of cost is provided to search the supervisor with minimal control and observe cost. A simulation example shows the correctness and effectiveness of the method.