  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.
