A merging method for the siphon-based FMS maximally permissive controllers with simpler structures

It has been a hot race to design optimal controllers to be maximally permissive with fewest monitors in the shortest amount of time for flexible manufacturing systems modelled by Petri nets. Recent maximally permissive deadlock prevention controls for systems of simple sequential processes with resources reduce the computation burden by considering only a small portion of all forbidding markings and employ much fewer monitors by a linear integer programming method. Maximal permissiveness is ensured by not forbidding any live state. However, it still requires costly reachability analysis. Our previous work avoids reachability analysis by classifying siphons and adding monitors to critical siphons only. However, some live states may get lost and the number of monitors required is as many as that of critical siphons. This paper proposes a method to merge several monitors into a single one while not losing the live states. It achieves the same best results in the existing literature while avoiding the time-consuming reachability analysis which does not scale well with the large size of the nets.