  Deep learning has enjoyed much recent success, and applying state-of-the-art
model learning methods to controls is an exciting prospect. However, there is a
strong reluctance to use these methods on safety-critical systems, which have
constraints on safety, stability, and real-time performance. We propose a
framework which satisfies these constraints while allowing the use of deep
neural networks for learning model uncertainties. Central to our method is the
use of Bayesian model learning, which provides an avenue for maintaining
appropriate degrees of caution in the face of the unknown. In the proposed
approach, we develop an adaptive control framework leveraging the theory of
stochastic CLFs (Control Lyapunov Functions) and stochastic CBFs (Control
Barrier Functions) along with tractable Bayesian model learning via Gaussian
Processes or Bayesian neural networks. Under reasonable assumptions, we
guarantee stability and safety while adapting to unknown dynamics with
probability 1. We demonstrate this architecture for high-speed terrestrial
mobility targeting potential applications in safety-critical high-speed Mars
rover missions.
