  This paper presents a novel approach for the safe control design of systems
with parametric uncertainties in both drift terms and control-input matrices.
The method combines control barrier functions and adaptive laws to generate a
safe controller through a nonlinear program with an explicitly given
closed-form solution. The proposed approach verifies the non-emptiness of the
admissible control set independently of online parameter estimations, which can
ensure the safe controller is singularity-free. A data-driven algorithm is also
developed to improve the performance of the proposed controller by tightening
the bounds of the unknown parameters. The effectiveness of the control scheme
is demonstrated through numerical simulations.
