Exploiting symmetry of discrete-event systems with parallel components by relabeling

We consider discrete-event systems (DES) consisting of parallel arrays of machines and buffers. The machines are divided into groups in each of which the members have identical (isomorphic) structure. This feature allows event relabeling of the machines in a given group to a standard prototype machine. With respect to buffer specifications (prohibiting overflow and underflow) it is shown that optimal supervisory control of the original DES (with many machines) can be reduced to control of the much smaller collection of prototype machines. The result is a small “template” supervisor which is proved to be independent of the total number of original component machines, as long as the buffer sizes are held fixed. This result is applied to efficient reconfiguration triggered by the addition or removal of machines.