Suboptimal liveness-enforcing supervisor design for a class of generalised Petri nets using partial siphon enumeration and mathematical programming

This article develops a deadlock prevention policy for a class of generalised Petri nets, which can well model a large class of flexible manufacturing systems. The analysis of such a system leads us to characterise the deadlock situations in terms of the insufficiently marked siphons in its generalised Petri-net model. The proposed policy is carried out in an iterative way. At each step a minimal siphon is derived from a maximal deadly marked siphon that is found by solving a mixed integer programming (MIP) problem. An algorithm is formalised that can efficiently compute such a minimal siphon from a maximal one. A monitor is added for a derived minimal siphon such that it is max-controlled if it is elementary with respect to the siphons that have been derived. The liveness of the controlled system is decided by the fact that no siphon can be derived due to the MIP solution. After a liveness-enforcing net supervisor computed without complete siphon enumeration, the output-arcs of the additional monitors are rearranged such that the monitors act while restricting the system less. Examples are presented to demonstrate the proposed method.