  Safety constraints of nonlinear control systems are commonly enforced through
the use of control barrier functions (CBFs). Uncertainties in the dynamic model
can disrupt forward invariance guarantees or cause the state to be restricted
to an overly conservative subset of the safe set. In this paper, adaptive deep
neural networks (DNNs) are combined with CBFs to produce a family of
controllers that ensure safety while learning the system's dynamics in
real-time without the requirement for pre-training. By basing the least squares
adaptation law on a state derivative estimator-based identification error, the
DNN parameter estimation error is shown to be uniformly ultimately bounded. The
convergent bound on the parameter estimation error is then used to formulate
CBF-constraints in an optimization-based controller to guarantee safety despite
model uncertainty. Furthermore, the developed method is applicable for use
under intermittent loss of state-feedback. Comparative simulation results
demonstrate the ability of the developed method to ensure safety in an adaptive
cruise control problem and when feedback is lost, unlike baseline methods.
