Identification of fractional order systems using modulating functions method

Da-Yan Liu 1 Taous-Meriem Laleg-Kirati 1 Olivier Gibaru 2, 3 Wilfrid Perruquetti 4, 2
2 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
4 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
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.
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  • HAL Id : hal-00801425, version 1
  • ARXIV : 1303.3877

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Da-Yan Liu, Taous-Meriem Laleg-Kirati, Olivier Gibaru, Wilfrid Perruquetti. Identification of fractional order systems using modulating functions method. 2013 American Control Conference, 2013, Jun 2013, Washington, DC, United States. ⟨hal-00801425⟩

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