Extended Adaptive Observer for Linear Systems with Overparametrization

TL;DR

This paper introduces an exponentially stable extended adaptive observer for linear systems with unknown parameters and overparameterization, capable of reconstructing physical states and disturbances under weak excitation conditions.

Contribution

It presents a novel observer that reconstructs original system states directly, unlike existing methods that focus on observer canonical form states.

Findings

Successfully reconstructs original states and disturbances in simulations.

Operates under weak regressor excitation conditions.

Demonstrates improved stability and accuracy over prior methods.

Abstract

Exponentially stable extended adaptive observer is proposed for a class of linear time-invariant systems with unknown parameters and overparameterization. It allows one to reconstruct unmeasured states and bounded external disturbance produced by a known linear exosystem with unknown initial conditions if a weak requirement of regressor finite excitation is met. In contrast to the existing solutions, the proposed observer reconstructs the original (physical) states of the system rather than the virtual one of its observer canonical form. Simulation results to validate the developed theory are presented.