Une méthode d'identification pour un système linéaire à retards

François Ollivier; Saïd Moutaouakil; Brahim Sadik

doi:10.1016/j.crma.2007.04.012

Une méthode d'identification pour un système linéaire à retards

Translated title of the contribution: A method of identification for a linear delays system

François Ollivier
, Saïd Moutaouakil
, Brahim Sadik

INRIA-Futurs and Xyleme
Cadi Ayyad University

Research output: Contribution to journal › Article › peer-review

Abstract

We provide a class of methods for the identification of a linear system with delay of the shape x⁽ⁿ⁾ (t) = ∑_{i = 0} ^{n - 1} a_i x⁽ⁱ⁾ (t) + b u (t - h). They allow the simultaneous identification of the parameters and delay, the observation of x and its derivatives, knowing only generic input u and output x. They are robust to the noise. Used in continuous time, they may follow the evolution of slowly varying parameters and noise. The method may be generalized to systems with two or more delays, e.g. x^″ (t) + a x (t - R₁) = b u (t - R₂). To cite this article: F. Ollivier et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

Translated title of the contribution	A method of identification for a linear delays system
Original language	French
Pages (from-to)	709-714
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	344
Issue number	11
DOIs	https://doi.org/10.1016/j.crma.2007.04.012
Publication status	Published - 1 Jun 2007
Externally published	Yes

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title = "Une m{\'e}thode d'identification pour un syst{\`e}me lin{\'e}aire {\`a} retards",

abstract = "We provide a class of methods for the identification of a linear system with delay of the shape x(n) (t) = ∑i = 0 n - 1 ai x(i) (t) + b u (t - h). They allow the simultaneous identification of the parameters and delay, the observation of x and its derivatives, knowing only generic input u and output x. They are robust to the noise. Used in continuous time, they may follow the evolution of slowly varying parameters and noise. The method may be generalized to systems with two or more delays, e.g. x″ (t) + a x (t - R1) = b u (t - R2). To cite this article: F. Ollivier et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).",

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T1 - Une méthode d'identification pour un système linéaire à retards

AU - Ollivier, François

AU - Moutaouakil, Saïd

AU - Sadik, Brahim

PY - 2007/6/1

Y1 - 2007/6/1

N2 - We provide a class of methods for the identification of a linear system with delay of the shape x(n) (t) = ∑i = 0 n - 1 ai x(i) (t) + b u (t - h). They allow the simultaneous identification of the parameters and delay, the observation of x and its derivatives, knowing only generic input u and output x. They are robust to the noise. Used in continuous time, they may follow the evolution of slowly varying parameters and noise. The method may be generalized to systems with two or more delays, e.g. x″ (t) + a x (t - R1) = b u (t - R2). To cite this article: F. Ollivier et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

AB - We provide a class of methods for the identification of a linear system with delay of the shape x(n) (t) = ∑i = 0 n - 1 ai x(i) (t) + b u (t - h). They allow the simultaneous identification of the parameters and delay, the observation of x and its derivatives, knowing only generic input u and output x. They are robust to the noise. Used in continuous time, they may follow the evolution of slowly varying parameters and noise. The method may be generalized to systems with two or more delays, e.g. x″ (t) + a x (t - R1) = b u (t - R2). To cite this article: F. Ollivier et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

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DO - 10.1016/j.crma.2007.04.012

M3 - Article

AN - SCOPUS:34249908370

SN - 1631-073X

VL - 344

SP - 709

EP - 714

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 11

ER -

Une méthode d'identification pour un système linéaire à retards

Abstract

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