  This paper studies the design of controllers that guarantee stability and
safety of nonlinear control affine systems with parametric uncertainty in both
the drift and control vector fields. To this end, we introduce novel classes of
robust control barrier functions (RCBF) and robust control Lyapunov functions
(RCLF) that facilitate the synthesis of safety-critical controllers in the
presence of parametric uncertainty using quadratic programming. Since the
initial bounds on the system uncertainty may be highly conservative, we present
a data-driven approach to reducing such bounds using input-output data
collected online. In particular, we leverage an integral set-membership
identification algorithm that iteratively shrinks the set of possible system
parameters online and guarantees stability and safety during learning. The
efficacy of the developed approach is illustrated on two numerical examples.
