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Some Stochastic Gradient Algorithms for Hammerstein Systems with Piecewise Linearity

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Abstract

Some stochastic gradient (SG) algorithms for Hammerstein systems with piecewise linearity are developed in this paper. Due to the complexity of the nonlinear structure, the key term separation is used to transfer the nonlinear model into a regression model, and then, some SG algorithms are proposed for this model. Since the SG algorithm has slow convergence rate, a forgetting factor SG algorithm and an Aitken SG algorithm are provided. Compared with the forgetting factor SG algorithm, the Aitken SG algorithm has smaller variance of estimation error, which means the Aitken SG algorithm is more effective. Two simulation examples are provided to show the effectiveness of the proposed algorithms.

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Data Availability Statement

All data generated or analyzed during this study are included in this article.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 61973137), the Funds of the Science and Technology on Near-Surface Detection Laboratory (No. TCGZ2019A001) and the Fundamental Research Funds for the Central Universities (No. JUSRP22016).

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Authors and Affiliations

  1. School of Science, Jiangnan University, Wuxi, 214122, People’s Republic of China

    Yan Pu, Yongqing Yang & Jing Chen

  2. School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, People’s Republic of China

    Yan Pu

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Correspondence to Yongqing Yang.

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Pu, Y., Yang, Y. & Chen, J. Some Stochastic Gradient Algorithms for Hammerstein Systems with Piecewise Linearity. Circuits Syst Signal Process 40, 1635–1651 (2021). https://doi.org/10.1007/s00034-020-01554-z

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