Dynamic Regressor Extension and Mixing-based Re-design of Adaptive Observer for Affine Systems

TL;DR

This paper introduces a novel adaptive observer design for affine systems using dynamic regressor extension and mixing, improving parameter convergence and excitation properties without requiring the state transition matrix.

Contribution

It presents a reduced-order adaptive observer re-designed with a new regressor dynamics approach, eliminating the need for the state transition matrix and enhancing convergence.

Findings

Improved parameter convergence despite lack of transition matrix

Enhanced excitation properties of the extension matrix

Reduced-order observer design successfully implemented

Abstract

The dynamic regressor extension and mixing procedure is employed to redesign a conventional adaptive observer algorithm for affine systems. A reduced-order observer is designed without the construction of the state transition matrix. The dynamics of the regressor are redesigned to incorporate feedback from its extension, transforming the regressor dynamics into a perturbed damped nonlinear oscillator form. This introduces some flexibility in reducing the degradation of parameter convergence due to the lack of the transition matrix and in enhancing the excitation property of the extension matrix.