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Gradient-Based Identification Methods for Hammerstein Nonlinear ARMAX Models

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An Erratum to this article was published on 25 January 2007

Abstract

Two identification algorithms, an iterative gradient and a recursive stochastic gradient based, are developed for a Hammerstein nonlinear ARMAX model, a linear dynamical block following a memoryless nonlinear block. The basic idea is to use the gradient search principle, to replace unmeasurable noise terms in the information vectors by their estimates, and to compute iteratively or recursively the noise estimates based on the obtained parameter estimates. Convergence analysis of the recursive stochastic gradient algorithm indicates that the parameter estimation error consistently converges to zero under certain conditions. The simulation results show the effectiveness of the proposed algorithms.

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Authors and Affiliations

  1. Control Science and Engineering Research Center, Southern Yangtze University, Wuxi, 214122, China

    Feng Ding

  2. Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, Canada, S7N 5A9

    Yang Shi

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada, T6G 2V4

    Tongwen Chen

Authors
  1. Feng Ding
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  2. Yang Shi
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  3. Tongwen Chen
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Corresponding author

Correspondence to Tongwen Chen.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s11071-006-9159-0.

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Ding, F., Shi, Y. & Chen, T. Gradient-Based Identification Methods for Hammerstein Nonlinear ARMAX Models. Nonlinear Dyn 45, 31–43 (2006). https://doi.org/10.1007/s11071-005-1850-z

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  • DOI: https://doi.org/10.1007/s11071-005-1850-z

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