<p>This work focuses on the identification problem for the class of interconnected nonlinear systems, in particular fractional-order Hammerstein–Wiener systems with colored noise. Such systems consist of a fractional-order dynamic linear subsystem embedded between two static nonlinear blocks. The linear subsystem is described on the basis of the fractional calculus theory. A filter-based recursive least squares algorithm is proposed by combining the auxiliary model principles with the filtering technique. The algorithm developed serves to jointly estimate all model parameters, including the noise model parameters, starting from filtered input and output data. A complete convergence analysis is presented to prove the consistency of the algorithm. The simulation and benchmark results confirm the effectiveness of the developed approach in offering consistent parameter estimates with high accuracy and fast convergence speed compared to existing methods in the literature.</p>

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Identification of interconnected nonlinear systems with colored noise using fractional calculus

  • Soumaya Marzougui,
  • Saida Bedoui,
  • Kamel Abderrahim

摘要

This work focuses on the identification problem for the class of interconnected nonlinear systems, in particular fractional-order Hammerstein–Wiener systems with colored noise. Such systems consist of a fractional-order dynamic linear subsystem embedded between two static nonlinear blocks. The linear subsystem is described on the basis of the fractional calculus theory. A filter-based recursive least squares algorithm is proposed by combining the auxiliary model principles with the filtering technique. The algorithm developed serves to jointly estimate all model parameters, including the noise model parameters, starting from filtered input and output data. A complete convergence analysis is presented to prove the consistency of the algorithm. The simulation and benchmark results confirm the effectiveness of the developed approach in offering consistent parameter estimates with high accuracy and fast convergence speed compared to existing methods in the literature.