Exploiting Symmetry of Discrete-Event Systems by Relabeling and Reconfiguration

Symmetric discrete-event systems (DESs) are composed of groups of identical components (machines) and buffers. As every component in each group has the same structure, they can be relabeled to a 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. With buffer sizes fixed, the result is a small invariant supervisor which is independent of the total number of original machines. We analyze the underlying reason for this invariance property and apply the result of the invariant reduced supervisor to efficient reconfiguration triggered by the addition or removal of machines and increase or decrease of the buffer capacity.