A Note on Relative Observability in Coordination Control

TL;DR

This paper explores relative observability in coordination control of discrete-event systems, showing it is a practical, union-closed condition that can replace normality for designing controllable and observable sublanguages.

Contribution

It demonstrates that conditional strong relative observability is a weaker alternative to conditional normality, with a distributive procedure for computing suitable sublanguages.

Findings

Conditional strong relative observability is weaker than conditional normality.

A distributive procedure for computing controllable and observable sublanguages.

Relative observability is closed under language unions.

Abstract

Relative observability has been introduced and studied in the framework of partially observed discrete-event systems as a condition stronger than observability, but weaker than normality. However, unlike observability, relative observability is closed under language unions, which makes it interesting for practical applications. In this paper, we investigate this notion in the framework of coordination control. We prove that conditional normality is a stronger condition than conditional (strong) relative observability, hence conditional strong relative observability can be used in coordination control instead of conditional normality, and present a distributive procedure for the computation of a conditionally controllable and conditionally observable sublanguage of the specification that contains the supremal conditionally strong relative observable sublanguage.