Synthesis of Petri nets controller for the constraints involving marking vector and Parikh vector

The problem of enforcing linear inequality constraints involving the marking vector and the Parikh vector on a discrete event system (DES) modeled by Petri nets (PN) is discussed in this paper. A novel method for design of controller enforcing the constraints is presented. First the constraints involving the marking and the Parikh vector are transformed into the constraints involving Parikh vector only, and then the controller is constructed based on the viewpoint that a place can be seen as a linear inequality constraint on Parikh vector. The method is proved to be simpler and more efficient than the method presented by Iordache and Moody through an applied instance that was also cited by Moody et al., and holds remarkable advantage especially for large systems.