  This paper introduces a parameter adaptation-based control law for a class of
nonlinear, control-affine, safety-critical systems subject to additive,
parameter-affine model uncertainty. It is shown that the uncertainty is learned
in fixed-time, i.e., within a finite time independent of the initial parameter
estimates, without requiring persistence of excitation or rank conditions on
the associated regressor matrix. A monotonically decreasing bound on the error
of the estimated uncertainty is derived and used in the proposed control
barrier function-based control law for guaranteed safety of the system
trajectories. It is then proven that the parameter adaptation law is robust to
bounded measurement noise and non-parametric perturbations to the system in
that the estimated uncertainty still converges to a known neighborhood of the
true uncertainty in fixed-time. The advantages of the approach are highlighted
in a comparative numerical study, and the method is validated on a quadrotor
trajectory-tracking problem subject to safety requirements and an unknown wind
field.
