On Preserving Observation Properties of the Reduced Supervisor in Discrete-Event Systems
For researchers in discrete-event systems, this is an incremental theoretical extension of existing supervisor reduction methods.
The paper proves that a reduced supervisor in discrete-event systems preserves observation properties (normality and relative observability) by self-looping unobservable events at certain states, enabling the identification of a natural projection for relative observability.
Supervisor reduction procedure can be used to construct the reduced supervisor with a reduced number of states in discrete-event systems. The main concepts which are used in this procedure are control consistency of states, control cover, induced supervisor, and normality of the reduced supervisor w.r.t. the original supervisor. In this paper, it is proved that the reduced supervisor, constructed by the proposed method in [9], preserves the observation properties, i.e. normality and relative observability, by self looping corresponding unobservable events at some states of the reduced supervisor. This property can be applied to find a natural projection, under which the supervisor is relative observable.