On polynomial explicit partial estimator design for nonlinear systems with parametric uncertainties

TL;DR

This paper proposes a data-driven polynomial partial estimator design for nonlinear systems with uncertainties, demonstrating its effectiveness over machine learning methods especially with limited data.

Contribution

It introduces a novel sparse polynomial identification framework for nonlinear systems with parametric uncertainties, validated through comparative examples.

Findings

Superiority of the proposed sparse polynomial scheme with small data sets

Effective handling of parametric uncertainties in nonlinear systems

Validation against machine/deep learning methods

Abstract

This paper investigates the idea of designing data-driven partial estimators for nonlinear systems showing parametric uncertainties using sparse multivariate polynomial relationships. A general framework is first presented and then validated on two illustrative examples with comparison to different possible Machine/Deep-Learning based alternatives. The results suggests the superiority of the proposed sparse identification scheme, at least when the learning data is small.