Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions

This letter proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating the locations and the amplitudes of a multi-pointwise i...

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Bibliographic Details
Published in:IEEE control systems letters 2018-01, Vol.2 (1), p.7-12
Main Authors: Belkhatir, Zehor, Laleg-Kirati, Taous-Meriem
Format: Article
Language:English
Subjects:
Differential equations
Estimation
History
Linear fractional order systems
Mathematical model
modulating functions method
Newton method
Noise measurement
Nonlinear systems
pointwise input
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Summary:This letter proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating the locations and the amplitudes of a multi-pointwise input is decoupled into two algebraic systems of equations. The first system is nonlinear and solves for the time locations iteratively, whereas the second system is linear and solves for the input's amplitudes. Second, closed form formulas for both the time location and the amplitude are provided in the particular case of single point input. Finally, numerical examples are given to illustrate the performance of the proposed technique in both noise-free and noisy cases. The joint estimation of pointwise input and fractional differentiation orders is also presented. Furthermore, a discussion on the performance of the proposed algorithm is provided.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2017.2720681