Universal approximation using differentiators and application to feedback control

TL;DR

This paper introduces two universal approximation methods using integral-chain differentiators and extended observers for nonlinear systems, enabling uncertainty approximation and state estimation, with noise suppression and validated through simulations.

Contribution

The paper proposes novel approximation techniques that combine uncertainty estimation and state observation without full state knowledge, outperforming traditional fuzzy and RBF neural network methods.

Findings

Methods effectively approximate uncertainties and estimate states.

Integral-chain differentiator suppresses noise thoroughly.

Validated through computer simulations in feedback control.

Abstract

In this paper, we consider the problems of approximating uncertainties and feedback control for a class of nonlinear systems without full-known states, and two approximation methods are proposed: universal approximation using integral-chain differentiator or extended observer. Comparing to the approximations by fuzzy system and radial-based-function (RBF) neural networks, the presented two methods can not only approximate universally the uncertainties, but also estimate the unknown states. Moreover, the integral-chain differentiator can restrain noises thoroughly. The theoretical results are confirmed by computer simulations for feedback control.