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Fractional gradient descent algorithms for systems with outliers: A matrix fractional derivative or a scalar fractional derivative

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  • Cao, Yuan
  • Su, Shuai

Abstract

Two gradient descent based fractional methods are proposed for systems with outliers in this paper. The outliers in the collected data usually causes biased estimates, resulting in a poor identification model. Tradition fractional gradient descent (FGD) algorithm has an assumption that the fractional derivative is a scalar, which leads to slow convergence rates, especially for systems with an ill-conditioned matrix. The proposed algorithms in this paper have several advantages over the traditional identification methods: (1) can get unbiased estimates; (2) have faster convergence rates; (3) enrich the FGD estimation framework. Simulation examples demonstrate the effectiveness of the proposed algorithms.

Suggested Citation

  • Cao, Yuan & Su, Shuai, 2023. "Fractional gradient descent algorithms for systems with outliers: A matrix fractional derivative or a scalar fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007828
    DOI: 10.1016/j.chaos.2023.113881
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    References listed on IDEAS

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    1. Zhu, Linhe & Tang, Yuxuan & Shen, Shuling, 2023. "Pattern study and parameter identification of a reaction-diffusion rumor propagation system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
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    Cited by:

    1. Khan, Taimoor Ali & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Mehmood, Khizer & Hsu, Chung-Chian & Raja, Muhammad Asif Zahoor, 2024. "Design of Runge-Kutta optimization for fractional input nonlinear autoregressive exogenous system identification with key-term separation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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