  In many control system applications, state constraint satisfaction needs to
be guaranteed within a prescribed time. While this issue has been partially
addressed for systems with known dynamics, it remains largely unaddressed for
systems with unknown dynamics. In this paper, we propose a Gaussian
process-based time-varying control method that leverages backstepping and
control barrier functions to achieve safety requirements within prescribed time
windows for control affine systems. It can be used to keep a system within a
safe region or to make it return to a safe region within a limited time window.
These properties are cemented by rigorous theoretical results. The
effectiveness of the proposed controller is demonstrated in a simulation of a
robotic manipulator.
