Identification of fractional order systems using modulating functions method

Handle URI:
http://hdl.handle.net/10754/565867
Title:
Identification of fractional order systems using modulating functions method
Authors:
Liu, Dayan; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 ) ; Gibaru, O.; Perruquetti, Wilfrid
Abstract:
The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2013 American Control Conference
Conference/Event name:
American Control Conference (ACC), 2013
Issue Date:
Jun-2013
DOI:
10.1109/ACC.2013.6580077
ARXIV:
arXiv:1303.3877v1
Type:
Conference Paper
ISSN:
07431619
ISBN:
9781479901777
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLiu, Dayanen
dc.contributor.authorLaleg-Kirati, Taous-Meriemen
dc.contributor.authorGibaru, O.en
dc.contributor.authorPerruquetti, Wilfriden
dc.date.accessioned2015-08-11T13:44:09Zen
dc.date.available2015-08-11T13:44:09Zen
dc.date.issued2013-06en
dc.identifier.isbn9781479901777en
dc.identifier.issn07431619en
dc.identifier.doi10.1109/ACC.2013.6580077en
dc.identifier.urihttp://hdl.handle.net/10754/565867en
dc.description.abstractThe modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.titleIdentification of fractional order systems using modulating functions methoden
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journal2013 American Control Conferenceen
dc.conference.date17-19 June 2013en
dc.conference.nameAmerican Control Conference (ACC), 2013en
dc.conference.locationWashington, DCen
dc.identifier.arxividarXiv:1303.3877v1en
kaust.authorLiu, Dayanen
kaust.authorLaleg-Kirati, Taous-Meriemen
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