Estimation of Unknown Parameters in Presence of Perturbations and Noises with Application to GPEBO Design

TL;DR

This paper introduces three new online parameter estimation methods that achieve exponential convergence despite perturbations and noise, improving GPEBO design for nonlinear systems.

Contribution

It presents novel estimation laws that overcome limitations of existing methods, ensuring exponential convergence even with noisy measurements and partial regressor independence.

Findings

Proposed estimation laws ensure exponential convergence to a small neighborhood.

One law enhances GPEBO performance under noisy output measurements.

Theoretical results are validated through examples and mathematical modeling.

Abstract

A problem of online estimation of unknown parameters is considered for a linear regression equation, which is affected by an additive perturbation that can be caused by measurement noise (that corrupts regressor and regressand), as well as external perturbations. Known approaches to solve this problem typically have one of the following disadvantages: 1) they ensure convergence of a parametric error to a compact set with non-adjustable bound, 2) independence of all system regressor elements from the perturbation/noise is required to annihilate them, 3) an instrumental variable is needed to be selected. On the basis of the novel perturbation annihilation procedure, in the present paper, we propose three new estimation laws, which are free from the above-mentioned drawbacks and ensure exponential convergence of the parametric error to an arbitrarily small neighborhood of zero, particularly, in case more than a half (not all) of the regressor elements are independent from additive perturbation. One of the proposed estimation laws is used for the design of Generalized Parameter Estimation-Based Observer (GPEBO) for nonlinear affine systems to enhance GPEBO performance in case when the measured system output is corrupted by noise. The theoretical results are supported by examples and mathematical modelling.