Non-blocking supervisors synthesis for a class of discrete event systems based on two-stage deadlock control

In this paper we deal with deadlock problems for a class of resource allocation systems, namely G-system, which allows multiple resource acquisitions and flexible routings with machining, assembly, and disassembly operations. A deadlock prevention methodology that is an iterative approach consisting of two stages is proposed. The first one is called siphons control, which is to add a control place to the original net for each insufficiently marked minimal siphon. The objective is to prevent a minimal siphon from being insufficiently marked. The second one, called control-induced siphons control, is to add a control place to the augmented net with its output arcs connecting to source transitions, which assures that there is no new insufficiently marked siphon generated. A mixed integer programming approach is adopted for generalized Petri nets to obtain an insufficiently marked minimal siphon from the maximal deadly marked siphon. This way avoids complete siphon enumeration that is much more time-consuming for a sizeable plant model than the existing method. This paper makes the application of presented deadlock control methods to G-systems.