Supremal Normal Sublanguages in Hierarchical Supervisory Control

In this paper, we study hierarchical supervisory control with partial observations. In particular, we are interested in preservation of supremal normal and supremal controllable and normal sublanguages from the abstracted system (high level) in the original (low level) system. Sufficient conditions are formulated under which the supremal normal or the supremal controllable and normal sublanguage computed at the high level (for the abstracted plant) is implementable at the low level, i.e., in the original plant.