Control Algorithm Using a Revised MIP Method to Deal with Livelocks in S~4R of Petri Nets

Livelocks, like deadlocks, can result in serious results in running process of flexible manufacturing systems(FMSs). Current deadlock control policies(DCPs) based on mixed integer programming(MIP) cannot detect siphons that cause and cope with livelocks in Petri nets. This study proposes a revised mixed integer programming(RMIP) method to directly solve the new smart siphons(NSSs) associated with livelocks in a system of sequential systems with shared resources(S~4 R), a typical subclass of generalized Petri net models. Accordingly,the solved NSSs are max'-controlled by adding the corresponding control places(CPs). As a result, an original S~4 R system with livelocks can be converted into the live controlled Petri net system. The related theoretical analysis and an example are given to demonstrate the proposed RMIP and the corresponding control algorithm(CA).