  A new adaptive observer is proposed for a certain class of nonlinear systems
with bounded unknown input and parametric uncertainty. Unlike most existing
solutions, the proposed approach ensures asymptotic convergence of the unknown
parameters, state and perturbation estimates to an arbitrarily small
neighborhood of the equilibrium point. The solution is based on the novel
augmentation of a high-gain observer with the dynamic regressor extension and
mixing (DREM) procedure enhanced with a perturbation annihilation algorithm.
The aforementioned properties of the proposed solution are verified via
numerical experiments.
