Robust liveness-enforcing supervisor for Petri nets with unreliable resources based on mixed integer programming

Petri nets, as an effective mathematical tool, have been intensively used in modeling and analyzing automated manufacturing systems (AMSs). Many deadlock control policies have been proposed for AMSs, but most of them assume that resources never fail during product processing. However, resource failures may happen in a real world, which may invalidate existing control policies. This paper concentrates on robust liveness-enforcing supervisor design for a system of simple sequential processes with multiple unreliable resources. Recovery subnets model resource failure and recovery, which are added to the holders of unreliable resource places. The proposed method consists of two steps. At the first step, a mixed integer programming (MIP) problem is developed to detect a strict minimal siphon that can be emptied. At the second step, an extended constraint set derived by the complementary set of a siphon is constructed. The siphon is controlled through the extended constraint set by adding a control place. The above two steps are executed in an iterative way until no new empty siphon is found and a robust liveness-enforcing supervisor can be obtained. Examples are used to expose the advantages of the proposed method.