Fractional order differentiation by integration  and error analysis in noisy environment

Liu, Da-Yan; Gibaru, Olivier; Perruquetti, Wilfrid; Laleg-Kirati, Taous-Meriem

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.1109/TAC.2015.2417852

Titre :

Fractional order differentiation by integration and error analysis in noisy environment

Auteur(s) :

Liu, Da-Yan [Auteur]
Laboratoire pluridisciplinaire de recherche en ingénierie des systèmes, mécanique et énergétique [PRISME]
Institut National des Sciences Appliquées - Centre Val de Loire [INSA CVL]
Gibaru, Olivier [Auteur]
Laboratoire des Sciences de l'Information et des Systèmes [LSIS]
Non-Asymptotic estimation for online systems [NON-A]
Perruquetti, Wilfrid [Auteur]

Non-Asymptotic estimation for online systems [NON-A]
Laleg-Kirati, Taous-Meriem [Auteur]
Estimation Modelling and ANalysis Group [KAUST-MCSE]

Titre de la revue :

IEEE Transactions on Automatic Control

Pagination :

2945 - 2960

Éditeur :

Institute of Electrical and Electronics Engineers

Date de publication :

2015

ISSN :

0018-9286

Mot(s)-clé(s) en anglais :

Jacobian matrices
Polynomials
Noise measurement
Noise
Robustness
Estimation error
Error analysis

Discipline(s) HAL :

Informatique [cs]/Automatique

Résumé en anglais : [en]

The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess. We propose to extend this method from the integer ...
Lire la suite >The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess. We propose to extend this method from the integer order to the fractional order to estimate the fractional order derivatives of noisy signals. Firstly, two fractional order differentiators are deduced from the Jacobi orthogonal polynomial filter, using the Riemann-Liouville and the Caputo fractional order derivative definitions respectively. Exact and simple formulae for these differentiators are given by integral expressions. Hence, they can be used for both continuous-time and discrete-time models in on-line or off-line applications. Secondly, some error bounds are provided for the corresponding estimation errors. These bounds allow to study the design parameters' influence. The noise error contribution due to a large class of stochastic processes is studied in discrete case. The latter shows that the differentiator based on the Caputo fractional order derivative can cope with a class of noises, whose mean value and variance functions are polynomial time-varying. Thanks to the design parameters analysis, the proposed fractional order differentiators are significantly improved by admitting a time-delay. Thirdly, in order to reduce the calculation time for on-line applications, a recursive algorithm is proposed. Finally, the proposed differentiator based on the Riemann-Liouville fractional order derivative is used to estimate the state of a fractional order system and numerical simulations illustrate the accuracy and the robustness with respect to corrupting noises.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL

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