Hierarchical Supervisory Control under Partial Observation: Normality

Abstract

Conditions preserving observability of specifications between the plant and its abstraction are fundamental for hierarchical supervisory control of discrete-event systems under partial observation. Observation consistency and local observation consistency were identified as such conditions. To preserve normality, only observation consistency is required. Although observation consistency preserves normality between the levels for normal specifications, we show that for specifications that are not normal, observation consistency does not guarantee that the supremal normal sublanguage computed on the low level and on the high level coincide. Therefore, we define modified observation consistency, under which the supremal normal sublanguages of different levels coincide. Since we show that the verification of (modified) observation consistency is PSPACE-hard for finite automata models and undecidable for systems slightly more expressive than finite automata, we further discuss two stronger conditions that are easy to verify, and hence of practical interest. We apply modified observation consistency in modular systems to guarantee that the global supervisor can be computed locally. In particular, we use the coordination control framework, where the global and local computations of supervisors coincide under the assumption that the coordinated events are all observable.

Hierarchical Supervisory Control Under Partial Observation: Normality

“…For comparison, we have included the monolithic approach (second column), and four monolithic approaches, one for each part of the specification (third column). The last column overviews the time and overall size of the high-level supervisors constructed by the hierarchical approach of Komenda and Masopust [32].…”

“…However, the algorithmic verification of MOC is a challenging open problem; the problem is known to be PSPACE-hard, but unknown to be decidable [32]. Therefore, we need other, easily-verifiable conditions that ensure MOC.…”

“…Modified observation consistency (MOC) is a concept of hierarchical supervisory control under partial observation developed to ensure hierarchical consistency [32].…”