Fractional order differentiation by ...
Document type :
Communication dans un congrès avec actes
Title :
Fractional order differentiation by integration: an application to fractional linear systems
Author(s) :
Liu, Da-Yan [Auteur]
Laleg-Kirati, Taous-Meriem [Auteur]
Gibaru, Olivier [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Laboratoire des Sciences de l'Information et des Systèmes [LSIS]
Laleg-Kirati, Taous-Meriem [Auteur]
Gibaru, Olivier [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Laboratoire des Sciences de l'Information et des Systèmes [LSIS]
Conference title :
6th IFAC Workshop on Fractional Differentiation and its Applications
City :
Grenoble
Country :
France
Start date of the conference :
2013-02-04
Publication date :
2013-02-04
HAL domain(s) :
Mathématiques [math]/Analyse numérique [math.NA]
English abstract : [en]
In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. ...
Show more >In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method.Show less >
Show more >In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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