A new algorithm for computing the supremal relatively observable sublanguage

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 we design an algorithm that computes the supremal sublanguage. This algorithm is formulated in terms of languages, thereby separating out the linguistic essence of the problem from the implementational aspects of state computation using automaton models. Exploiting the linguistic concept of support based on Nerode equivalence, we prove that for regular languages the algorithm is finitely convergent to the supremal sublanguage.