Relative Observability of Discrete-Event Systems and its Supremal Sublanguages

TL;DR

This paper introduces relative observability, a new concept in supervisory control of discrete-event systems, which allows for larger controlled behaviors by combining it with controllability, and provides algorithms to compute the supremal sublanguages.

Contribution

The paper defines relative observability, proves its properties, and develops algorithms to compute the supremal relatively observable and controllable sublanguages, expanding control possibilities.

Findings

Relative observability is preserved under set union.

The supremal relatively observable sublanguage is larger than the normal counterpart.

Algorithms successfully compute the supremal sublanguages, demonstrated on examples.

Abstract

We identify a new observability concept, called relative observability, in supervisory control of discrete-event systems under partial observation. A fixed, ambient language is given, relative to which observability is tested. Relative observability is stronger than observability, but enjoys the important property that it is preserved under set union; hence there exists the supremal relatively observable sublanguage of a given language. Relative observability is weaker than normality, and thus yields, when combined with controllability, a generally larger controlled behavior; in particular, no constraint is imposed that only observable controllable events may be disabled. We design algorithms which compute the supremal relatively observable (and controllable) sublanguage of a given language, which is generally larger than the normal counterparts. We demonstrate the new observability concept and algorithms with a Guideway and an AGV example.