We identify a new observability concept, called relative observability, in supervisory control of discrete-event systems under partial observation. A fixed, ambient language is given, relative to which observability is tested. Relative observability is stronger than observability, but enjoys the important property that it is preserved under set union; hence there exists the supremal relatively observable sublanguage of a given language. Relative observability is weaker than normality, and thus yields, when combined with controllability, a generally larger controlled behavior; in particular, no constraint is imposed that only observable controllable events may be disabled. We design algorithms which compute the supremal relatively observable (and controllable) sublanguage of a given language, which is generally larger than the normal counterparts. We demonstrate the new observability concept and algorithms with a Guideway and an AGV example.
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