Characterizing Safety: Minimal Barrier Functions from Scalar Comparison Systems.

摘要: Verifying set invariance has classical solutions stemming from the seminal work by Nagumo, and defining sets via a smooth barrier function constraint inequality results in computable flow conditions for guaranteeing invariance. While majority of these historic on consider boundary, recent control functions extended to entire set, although they required regularity function. This paper fully characterizes through \emph{minimal functions} directly appealing comparison result define condition over domain system. A considerable benefit this approach is removal assumptions also outlines necessary sufficient valid differential condition, giving minimum type approach. We show when minimal are