Relative coobservability for decentralised supervisory control of discrete-event systems

ABSTRACT

In this paper, we study the concept of relative coobservability in decentralised supervisory control of discrete-event systems under partial observation. This extends our previous work on relative observability from a centralised setup to a decentralised one. A fundamental concept in decentralised 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 a language-based algorithm to compute this supremal sublanguage; the algorithm allows straightforward implementation using off-the-shelf algorithms. 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.

KEYWORDS:

• Discrete-event systems
• supervisory control
• automata
• partial observation
• relative coobservability

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. That relative coobservability (or $\mathcal{I}$-fold relative observability) is stronger than disjunctive coobservability (Proposition 2.2) or conjunctive coobservability (Proposition 2.1) can also be proved by noting that it is stronger than a property called “local observability” (Takai et al., 2005): local observability requires that for each $i\in \mathcal{I}$, K be observable with respect to P _i , i.e. $\mathcal{I}$-fold observability, and is proved to be stronger than disjunctive and conjunctive coobservability.

Additional information

Funding

This work was partially supported by JSPS KAKENHI [grant number JP16K18122]; the National Nature Science Foundation of China [grant number 61403308]; the Natural Sciences and Engineering Research Council, Canada [grant number NSERC-DG-480599].