Active Controller Synthesis Of Discrete Event System Based On Petri Net Expansion Theory

Discrete event system is a manmade system which is driven by random events at discrete time. With the rapid development of technology, more and more manmade systems have the characteristics of discrete event system.Therefore, the study of discrete event systems has a high theoretical and practical value.The research of discrete event system mainly includes the system performance analysis and controller synthesis. This paper focuses on controller synthesis. As we know, automata and Petri nets are the two main tools for controller synthesis. Because of the advantages of Petri nets, the controller synthesis based on Petri nets has become more and more popular.Structure analysis and reachability graph method are the two main methods for controller synthesis of discrete event system. The reachability graph method can get the whole state information of a system, and the control policy obtained by the reachability graph method is always maximally permissive, but for some complex systems, the computational complexity is very high and the control structure is always complex; compared with reachability graph method, the computational complexity of structure analysis is lower and the control structure is more simple, but the control policy obtained by the structure analysis may not be maximally permissive. So, in this paper, we want to obtain a control policy which has low computational complexity and simple structure based on unfolding—a partial order method.Deadlock must be considered in the controller synthesis, because it can lead to paralysis. In these years, more and more authors consider the liveness of Petri nets rather than deadlock only. Liveness problem of Petri nets is an extension of the deadlock problem, Petri nets is live, and then it must be deadlock-free.Liveness can make the maximum utilization of the resources and also make sure that the Petri net is deadlock-free.In this paper, we firstly propose the cut graph G2 based on Petri nets unfolding, give and prove the necessary and sufficient conditions that characterize the original net’s liveness based on cut graph G2.Secondly, we propose and prove the necessary and sufficient conditions of the existence of liveness controller for a controllable bounded-ordinary Petrinets based on cut graph G1.At last, we introduce the definition of critical no-liveness markings and critical transitions, and obtain the logical liveness controller. Its control places are added to the unfolding. Then, we synthesize the equivalent structure controller which is added to the original Petri nets.