Soft Computing

, Volume 22, Issue 24, pp 8097–8106 | Cite as

Identification of neuro-fractional Hammerstein systems: a hybrid frequency-/time-domain approach

  • Mohammad-Reza Rahmani
  • Mohammad FarrokhiEmail author
Methodologies and Application


In this paper, modeling and identification of nonlinear dynamic systems using neuro-fractional Hammerstein model are considered. The proposed model consists of the neural networks (NNs) as the nonlinear subsystem and the fractional-order state space (FSS) as the linear subsystem. The identification procedure consists of a hybrid frequency-/time-domain approach based on the input–output data acquired from the system. First in the frequency domain, the fractional order and fractional degree of the FSS subsystem are determined offline using an iterative linear optimization algorithm. Then, in the time domain, the state-space matrices of the FSS as well as parameters of the NN are estimated using Lyapunov stability theory. Moreover, in order to use only the input–output data from the system, a fractional-order linear observer based on auxiliary model idea is utilized to estimate the system states. The convergence and stability analysis of the proposed method are provided. Simulating and experimental examples show superior performance of the proposed method as compared with the Hammerstein models reported in the literature.


Hammerstein model Fractional-order differential equations Neural networks Frequency-domain identification 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Electrical EngineeringIran University of Science and TechnologyTehranIran

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