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Conditions preserving observability of specifications between the plant andits abstraction are essential for hierarchical supervisory control ofdiscrete-event systems under partial observation. Observation consistency andlocal observation consistency were identified as such conditions. To preservenormality, only observation consistency is required. Although observationconsistency preserves normality between the levels for normal specifications,for specifications that are not normal, observation consistency is insufficientto guarantee that the supremal normal sublanguage computed on the low level andon the high level coincide. We define modified observation consistency, underwhich the supremal normal sublanguages of different levels coincide. We showthat the verification of (modified) observation consistency is PSPACE-hard forfinite automata and undecidable for slightly more expressive models than finiteautomata. Decidability of (modified) observation consistency is an openproblem. Hence we further discuss two stronger conditions that are easy toverify. Finally, we illustrate the conditions on an example of a railroadcontroller and on a case study of a part of an MRI scanner.

Hierarchical Supervisory Control under Partial Observation: Normality