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Recursive second-order Volterra filter based on Dawson function for chaotic memristor system identification

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In this paper, we propose a modified version of exponential cost function to improve the stability of adaptive algorithm, where the recursive algorithm is based on the Dawson function. The second-order Volterra (SOV) filter is incorporated into the proposed recursive algorithm, resulting the SOV-ExRLS algorithm, to achieve the improved performance in both \(\alpha \)-stable and Gaussian environments. Moreover, the mean and mean-square behavior of the SOV-ExRLS algorithm is analyzed. In particular, the proposed cExRLS-IDLMS method is convexly combined with the functional link artificial neural network filter to flexibly model the chaotic memristor system. Simulation studies verify the analytical findings and reveal enhanced identification performance of the proposed algorithms over the existing nonlinear algorithms.

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    This inequality is simply not reasonable in the general case. Consider the unknown system is persistently excited by \({\varvec{x}}(n)\), so that \({\varvec{\varUpsilon }}(n)>0\) for n and \({\varvec{x}}(n){\varvec{x}}^{\mathrm T}(n)\) is nonnegative-definite in (42). For this case, we show that \(\lambda _{\max }({{\varvec{A}}}{{\varvec{\varPi }}}) < {\mathrm {Tr}}({{\varvec{A}}}{{\varvec{\varPi }}})\).

  2. 2.

    Since the CExRLS-IDLMS algorithm is specifically designed for chaotic memristor system identification, we only compared the CExRLS-IDLMS algorithm with \(D=0\) in this section. The proposed SOV-ExRLS algorithm without time delay module, is not suitable for chaotic memristor system identification due to the effect of hysteresis. The SOV-ExRLS algorithm with time delay module is a new approach for hysteresis system, we will concern this method in the future.


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This work was partially supported by the National Science Foundation of P.R. China under Grant Nos. 61901285, 61901400, and 61701327, and China Postdoctoral Science Foundation under Grant 2018M640916.

The authors would like to thank the anonymous reviewers their constructive suggestions which have helped in improving the paper.

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Correspondence to Xiaomin Yang.

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Lu, L., Yang, X., Wang, W. et al. Recursive second-order Volterra filter based on Dawson function for chaotic memristor system identification. Nonlinear Dyn (2020). https://doi.org/10.1007/s11071-019-05459-8

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  • Volterra system
  • Adaptive filter
  • Recursive algorithm
  • Dawson function
  • Chaotic memristor system