Learning-based Prescribed-Time Safety for Control of Unknown Systems with Control Barrier Functions

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.