Nonlinear system identification using fractional Hammerstein–Wiener models

  • Karima HammarEmail author
  • Tounsia Djamah
  • Maamar Bettayeb
Original paper


The paper deals with identification of fractional order nonlinear systems based on Hammerstein–Wiener models. An output error approach is developed using the robust Levenberg–Marquardt algorithm. It presents the difficulty of the parametric sensitivity functions calculation which requires a heavy computational load at each iteration. To overcome this drawback, the fractional nonlinear system is reformulated under a regression form, and the gradient and the Hessian can be obtained in a closed form without using the parametric sensitivity functions. The method’s efficiency is confirmed on numerical simulations, and its feasibility is illustrated with its application to the modeling of an experimental arm robot.


Identification Nonlinear system Fractional order systems Hammerstein–Wiener model Levenberg–Marquardt algorithm Regression 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Karima Hammar
    • 1
    Email author
  • Tounsia Djamah
    • 1
  • Maamar Bettayeb
    • 2
  1. 1.Laboratoire de Conception et Conduite des Systèmes de, Production (L2CSP)UMMTOTizi-OuzouAlgérie
  2. 2.Department of Electrical and Computer EngineeringUniversity of Sharjah UAE and (CEIES), King Abdulaziz UniversityJeddahSaudi Arabia

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