A monitor solution to enforce legal transition firing sequences problems by using Petri nets

This paper focuses on supervisory control of a class of discrete event systems with known initial and destination states, whose evolution conforms to a set of specified linear or non-linear constraints. A supervisor is designed, which supervises the considered system to evolve and finally to reach the destination state with minimal costs without violating the specified constraints. A partial structure of the Petri net model of a system is first created by the constraints. Then, we find the destination state under the constraints by a search algorithm with least cost. A legal transition firing sequence can be found by solving integer programming problems with the constraints of the created model and the result of the search algorithm. Otherwise, a more exhaustive model is made under the limit of the constraints. Then, a set of control places is used to implement the transition sequence by introducing a set of complementary transitions. A mental game example is used to demonstrate the proposed approaches.