  Hamilton-Jacobi reachability methods for safety-critical control have been
well studied, but the safety guarantees derived rely on the accuracy of the
numerical computation. Thus, it is crucial to understand and account for any
inaccuracies that occur due to uncertainty in the underlying dynamics and
environment as well as the induced numerical errors. To this end, we propose a
framework for modeling the error of the value function inherent in
Hamilton-Jacobi reachability using a Gaussian process. The derived safety
controller can be used in conjuncture with arbitrary controllers to provide a
safe hybrid control law. The marginal likelihood of the Gaussian process then
provides a confidence metric used to determine switches between a least
restrictive controller and a safety controller. We test both the prediction as
well as the correction capabilities of the presented method in a classical
pursuit-evasion example.
