  Cyber-physical and autonomous systems are often equipped with mechanisms that
provide predictions/projections of future disturbances, e.g., road curvatures,
commonly referred to as preview or lookahead, but this preview information is
typically not leveraged in the context of deriving control barrier functions
(CBFs) for safety. This paper proposes a novel limited preview control barrier
function (LPrev-CBF) that avoids both ends of the spectrum, where on one end,
the standard CBF approach treats the (previewable) disturbances simply as
worst-case adversarial signals and on the other end, a recent Prev-CBF approach
assumes that the disturbances are previewable and known for the entire future.
Moreover, our approach applies to input-delay systems and has recursive
feasibility guarantees since we explicitly take input constraints/bounds into
consideration. Thus, our approach provides strong safety guarantees in a less
conservative manner than standard CBF approaches while considering a more
realistic setting with limited preview and input delays.
