Conditions for Hierarchical Supervisory Control under Partial Observation

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

Correction to “Relative Observability of Discrete-Event Systems and Its Supremal Sublanguages”

In this note, we make a few corrections to our previous paper “Relative Observability of Discrete-Event Systems and Its Supremal Sublanguages.” An error was found in the program that was originally used to compute the results of [1], Sec. V, Examples. Specifically, the generator displayed in Fig. 12, and multiple entries (4th, 7th row and 4th column) of Table 1 of [1] were incorrect. We present corrected results in the following