Probabilistic Safe Online Learning with Control Barrier Functions

Learning-based control schemes have recently shown great efficacy performing complex tasks. However, in order to deploy them in real systems, it is of vital importance to guarantee that the system will remain safe during online training and execution. We therefore need safe online learning frameworks able to autonomously reason about whether the current information at their disposal is enough to ensure safety or, in contrast, new measurements are required. In this paper, we present a framework consisting of two parts: first, an out-of-distribution detection mechanism actively collecting measurements when needed to guarantee that at least one safety backup direction is always available for use; and second, a Gaussian Process-based probabilistic safety-critical controller that ensures the system stays safe at all times with high probability. Our method exploits model knowledge through the use of Control Barrier Functions, and collects measurements from the stream of online data in an event-triggered fashion to guarantee recursive feasibility of the learned safety-critical controller. This, in turn, allows us to provide formal results of forward invariance of a safe set with high probability, even in a priori unexplored regions. Finally, we validate the proposed framework in numerical simulations of an adaptive cruise control system.