Adaptive Reconstruction of Nonlinear Systems States via DREM with Perturbation Annihilation

Abstract

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.

Figures (2)

• Figure 1: Dependence of $\omega \left( t \right)$ from $A$
• Figure 2: Behavior of errors $\left| {\tilde{x}_{2}\left( t \right)} \right|{\rm{,\;}}\left| {\tilde{\delta} \left( t \right)} \right|$ and $\tilde{\theta} \left( t \right)$ for different $T > 0$