Characterizations and Effective Computation of Supremal Relatively Observable Sublanguages

TL;DR

This paper introduces a new characterization and an effective computational method for finding the largest relatively observable sublanguage in supervisory control of discrete-event systems, ensuring better control under partial observation.

Contribution

It presents a novel characterization of relative observability and proposes operators to compute the supremal relatively observable sublanguage effectively, with proven finite convergence for regular languages.

Findings

Operator converges finitely for regular languages

Proposed operators are effectively computable

Demonstrated computational effectiveness through a case study

Abstract

Recently we proposed relative observability for supervisory control of discrete-event systems under partial observation. Relative observability is closed under set unions and hence there exists the supremal relatively observable sublanguage of a given language. In this paper we present a new characterization of relative observability, based on which an operator on languages is proposed whose largest fixpoint is the supremal relatively observable sublanguage. Iteratively applying this operator yields a monotone sequence of languages; exploiting the linguistic concept of support based on Nerode equivalence, we prove for regular languages that the sequence converges finitely to the supremal relatively observable sublanguage, and the operator is effectively computable. Moreover, for the purpose of control, we propose a second operator that in the regular case computes the supremal relatively observable and controllable sublanguage. The computational effectiveness of the operator is demonstrated on a case study.