On Preserving Observation Properties of the Reduced Supervisor in Discrete-Event Systems

TL;DR

This paper proves that a specific supervisor reduction method in discrete-event systems preserves key observation properties like normality and relative observability by adding self-loops for unobservable events.

Contribution

It demonstrates that the reduced supervisor maintains observation properties through self-looping unobservable events, enhancing supervisor reduction techniques.

Findings

Preserves normality and relative observability in reduced supervisors

Self-looping unobservable events at certain states maintains observation properties

Facilitates finding natural projections for relative observability

Abstract

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.