  Safety is always one of the most critical principles for a system to be
controlled. This paper investigates a safety-critical control scheme for
unknown structured systems by using the control barrier function (CBF) method.
Benefited from the dynamic regressor extension and mixing (DREM), an extended
element-wise parameter identification law is utilized to dismiss the
uncertainty. On the one hand, it is shown that the proposed control scheme can
always guarantee the safety in the identification process with noised signal
injection excitation, which was not considered in the previous study. On the
other hand, the element-wise estimation process in DREM can minimize
conservatism of the safe adaptive process compared to other existing adaptive
CBF algorithms. The stability as well as the forward invariance of the
presented safe control-estimation scheme is proved. Furthermore, the robustness
of the scheme under bounded disturbances is analyzed, where a robust CBF with
modest conditions is used to ensure safety. The framework is illustrated by
simulations on adaptive cruise control, where the slope resistance of the
following vehicle is robustly estimated in finite time against small
disturbances and the potential crash risk is avoided by the proposed safe
control scheme.
