  We present a novel technique for solving the problem of safe control for a
general class of nonlinear, control-affine systems subject to parametric model
uncertainty. Invoking Lyapunov analysis and the notion of fixed-time stability
(FxTS), we introduce a parameter adaptation law which guarantees convergence of
the estimates of unknown parameters in the system dynamics to their true values
within a fixed-time independent of the initial parameter estimation error. We
then synthesize the adaptation law with a robust, adaptive control barrier
function (RaCBF) based quadratic program to compute safe control inputs despite
the considered model uncertainty. To corroborate our results, we undertake a
comparative case study on the efficacy of this result versus other recent
approaches in the literature to safe control under uncertainty, and close by
highlighting the value of our method in the context of an automobile overtake
scenario.
