An improved deadlock control policy using elementary siphons and MIP approach

Based on elementary siphons of Petri nets and the mixed integer programming approach, an improved deadlock prevention policy is developed for S³PR. Siphons in such a plant Petri net model are divided into elementary and dependent ones. Our policy consists of two stages: siphon control and control-induced siphon control. At first stage, a monitor (control place) is added for each elementary siphon such that it is invariant-controlled. Due to the addition of monitors to plant model, control-induced siphons are possibly generated in the augmented S³PR, which is an RCN-merged net. The second stage sees that monitors are added to make always marked control-induced siphons in the resultant RCN-merged net without generating new control-induced siphons. Compared with our previous work, the deadlock prevention policy developed in this paper can lead to a structurally simple liveness-enforcing Petri net supervisor by adding only a small number of monitors and arcs. An FMS example is utilized to illustrate the proposed methods.