Reducing the Supervisory Control of Discrete-Event Systems under Partial Observation

Supervisor reduction procedure can be used to construct the reduced supervisor with a reduced number of states in discrete-event systems. However, it was proved that the reduced supervisor is control equivalent to the original supervisor with respect to the plant; it has not been guaranteed that the reduced supervisor and the original one are control equivalent under partial observation. In this paper, we extend the supervisor reduction procedure by considering partial observation; namely not all events are observable. A feasible supervisor which is constructed under partial observation becomes reduced based on control consistency of uncertainty sets of states, instead of the original supervisor. In order to construct a partial observation reduced supervisor, a partial observation control cover is constructed based on control consistency of uncertainty sets in the supervisor. Four basic functions are defined in order to capture the control and marking information on the uncertainty sets. In the resulting reduced supervisor, only observable events can cause state changes. The results are illustrated by some examples.