On the lower bound of monitor solutions of maximally permissive supervisors for a subclass α-S3PR of flexible manufacturing systems

Recently, a novel and computationally efficient method – based on a vector covering approach – to design optimal control places and an iteration approach that computes the reachability graph to obtain a maximally permissive liveness enforcing supervisor for FMS (flexible manufacturing systems) have been reported. However, it is unclear as to the relationship between the structure of the net and the minimal number of monitors required. This paper develops a theory to show that the minimal number of monitors required cannot be less than that of basic siphons in α-S3PR (systems of simple sequential processes with resources). This confirms that two of the three controlled systems by Chen et al. are of a minimal monitor configuration since they belong to α-S3PR and their number in each example equals that of basic siphons.