Natural Projections for the Synthesis of Non-Conflicting Supervisory Controllers

Supervisory controller synthesis for decomposable deterministic context free specification languages

“…However, both the natural and the MSA observer property are only sufficient conditions for non-blockingness. It was recently shown in [8] that there exists a necessary and sufficient condition to ensure nonblockingness in the case of abstraction-based control. This condition is defined as follows.…”

“…Definition 1 (adopted from [8]): Given a plant D P = P um , P and its projection D Po = P um,o , P o = p o (P um ), p o (P ) , define for any string w ∈ P um the sets…”

“…p o . Remark 2: In comparison to [8] we do not require the controller languages C o and C to be prefix-closed. Hence, following [3] and [7] we construct a marking instead of a non-marking nonblocking supervisor in the sense of [11].…”

“…Using their results, we show that the natural observer property and the local control consistency property are sufficient to ensure soundness in our setup. We furthermore enrich this result by substituting the natural observer property with a weaker condition introduced in [8], that we call conflict freeness. We furthermore show that in our setup these three conditions need to be checked for regular languages only, hence existing algorithms can be directly applied.…”