  Control barrier functions (CBFs) have recently introduced a systematic tool
to ensure system safety by establishing set invariance. When combined with a
nominal control strategy, they form a safety-critical control mechanism.
However, the effectiveness of CBFs is closely tied to the system model. In
practice, model uncertainty can compromise safety guarantees and may lead to
conservative safety constraints, or conversely, allow the system to operate in
unsafe regions. In this paper, we use Gaussian processes to mitigate the
adverse effects of uncertainty on high-order CBFs (HOCBFs). A properly
structured covariance function enables us to convert the chance constraints of
HOCBFs into a second-order cone constraint. This results in a convex
constrained optimization as a safety filter. We analyze the feasibility of the
resulting optimization and provide the necessary and sufficient conditions for
feasibility. The effectiveness of the proposed strategy is validated through
two numerical results.
