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Fractional Volterra LMS algorithm with application to Hammerstein control autoregressive model identification

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Abstract

In the present study, strength of fractional-order adaptive signal processing through fractional Volterra least mean square (FV-LMS) algorithm is exploited for Hammerstein nonlinear control autoregressive model (HN-CAR) identification. The FV-LMS method is a generalization of standard V-LMS by taking usual gradient as well as fractional derivative of cost function in the optimization process. The adaptive scheme FV-LMS is applied to HN-CAR systems for different variations of step size parameter, noise and fractional order. Comparative study of the optimized design variables by FV-LMS from true values of HN-CAR model is carried out using performance metrics of fitness and mean square error, to establish its effectiveness. The performance of the proposed scheme is validated through comparison with standard V-LMS based on multiple independent runs of the scheme.

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Authors and Affiliations

  1. Department of Electrical Engineering, International Islamic University, Islamabad, Pakistan

    Naveed Ishtiaq Chaudhary

  2. Hamdard Institute of Engineering and Technology, Hamdard University, Islamabad, Pakistan

    Muhammad Anwaar Manzar

  3. Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan

    Muhammad Asif Zahoor Raja

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  1. Naveed Ishtiaq Chaudhary
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  2. Muhammad Anwaar Manzar
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  3. Muhammad Asif Zahoor Raja
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Correspondence to Naveed Ishtiaq Chaudhary.

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Chaudhary, N.I., Manzar, M.A. & Raja, M.A.Z. Fractional Volterra LMS algorithm with application to Hammerstein control autoregressive model identification. Neural Comput & Applic 31, 5227–5240 (2019). https://doi.org/10.1007/s00521-018-3362-z

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