Non-asymptotic fractional order differentiators via an algebraic parametric method

TL;DR

This paper develops non-asymptotic fractional order differentiators using an algebraic parametric method applied to fractional Taylor series, providing simple formulas and demonstrating robustness and efficiency through numerical simulations.

Contribution

It introduces a novel algebraic parametric approach for fractional order differentiation based on fractional Taylor series and Jacobi polynomials, extending previous integer order methods.

Findings

Effective in noisy environments

Simple closed-form formulas derived

Demonstrated stability and efficiency in simulations

Abstract

Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations.