Relative Coobservability in Decentralized Supervisory Control of Discrete-Event Systems

TL;DR

This paper introduces the concept of relative coobservability for decentralized supervisory control of discrete-event systems, providing a well-behaved property that ensures the existence of a supremal sublanguage and an algorithm for its computation.

Contribution

It extends relative observability to decentralized systems, defines relative coobservability, and presents an algorithm to compute the supremal relatively coobservable sublanguage.

Findings

Relative coobservability is stronger than coobservability.

The supremal relatively coobservable sublanguage exists.

An algorithm for computing the supremal sublanguage is provided.

Abstract

We study the new concept of relative coobservability in decentralized supervisory control of discrete-event systems under partial observation. This extends our previous work on relative observability from a centralized setup to a decentralized one. A fundamental concept in decentralized supervisory control is coobservability (and its several variations); this property is not, however, closed under set union, and hence there generally does not exist the supremal element. Our proposed relative coobservability, although stronger than coobservability, is algebraically well-behaved, and the supremal relatively coobservable sublanguage of a given language exists. We present an algorithm to compute this supremal sublanguage. Moreover, relative coobservability is weaker than conormality, which is also closed under set union; unlike conormality, relative coobservability imposes no constraint on disabling unobservable controllable events.