Petri net cascade decomposition for supervisory control

In this paper, an effort has been made to find out whether or not a linear integer program can be applied to supervisory control for discrete event systems modeled by controlled Petri nets with some uncontrollable subloops. We find out that when the uncontrollable subnet has a cascade structure and each cascade subnet is a loop-free subnet or a state machine (maybe include some subloops), the online computation of control policies can be carried out by an linear integer program. For the sake of decomposing cascade structures of a Petri net, the paper also addresses the issue of the technique for Petri net cascade decomposition.