Conditions for Hierarchical Supervisory Control under Partial Observation

TL;DR

This paper investigates conditions for preserving observability in hierarchical supervisory control under partial observation, proving decidability of certain conditions and proposing a new condition to improve high-level control solutions.

Contribution

It establishes the decidability of observation consistency conditions for regular systems and introduces a modified condition to better preserve control solutions across hierarchy levels.

Findings

OC and LOC are decidable for regular systems.

Modified observation consistency preserves supremal normal sublanguages.

High-level solutions can outperform low-level solutions under the new condition.

Abstract

The fundamental problem in hierarchical supervisory control under partial observation is to find conditions preserving observability between the original (low-level) and the abstracted (high-level) plants. Two conditions for observable specifications were identified in the literature -- observation consistency (OC) and local observation consistency (LOC). However, the decidability of OC and LOC were left open. We show that both OC and LOC are decidable for regular systems. We further show that these conditions do not guarantee that supremal (normal or relatively observable) sublanguages computed on the low level and on the high level always coincide. To solve the issue, we suggest a new condition -- modified observation consistency -- and show that under this condition, the supremal normal sublanguages are preserved between the levels, while the supremal relatively observable high-level sublanguage is at least as good as the supremal relatively observable low-level sublanguage, i.e., the high-level solution may be even better than the low-level solution.