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A quasi fractional order gradient descent method with adaptive stepsize and its application in system identification

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  • Liu, Jianjun
  • Zhai, Rui
  • Liu, Yuhan
  • Li, Wenliang
  • Wang, Bingzhe
  • Huang, Liyuan

Abstract

In this paper, the fractional order gradient method (FOGM) is extended to the solution of high-dimensional function optimization problems. A quasi fractional order gradient descent method (QFOGDM) is proposed and then introduce an adaptive stepsize into QFOGDM. The theoretic analysis for convergence of QFOGDM is be done by three theorems. The numerical experiments for solving 15 unconstrained optimization benchmarks are compared to show its’ better performance. Meanwhile, the proposed algorithm is utilized to identify the parameters in the linear discrete deterministic systems and achieves a better convergence rate and accuracy.

Suggested Citation

  • Liu, Jianjun & Zhai, Rui & Liu, Yuhan & Li, Wenliang & Wang, Bingzhe & Huang, Liyuan, 2021. "A quasi fractional order gradient descent method with adaptive stepsize and its application in system identification," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    • Handle: RePEc:eee:apmaco:v:393:y:2021:i:c:s0096300320307505
    DOI: 10.1016/j.amc.2020.125797
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    References listed on IDEAS

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    4. Žecová, Monika & Terpák, Ján, 2015. "Heat conduction modeling by using fractional-order derivatives," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 365-373.
    5. Jiaxun Liu & Zuoxun Wang & Minglei Shu & Fangfang Zhang & Sen Leng & Xiaohui Sun, 2019. "Secure Communication of Fractional Complex Chaotic Systems Based on Fractional Difference Function Synchronization," Complexity, Hindawi, vol. 2019, pages 1-10, August.
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    Cited by:

    1. Wang, Ziyun & Wang, Xianzhe & Wang, Yan, 2024. "Orthotope-search-expansion-based extended zonotopic Kalman filter design for a discrete-time linear parameter-varying system with a dual-noise term," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    2. Han, Xiaohui & Dong, Jianping, 2023. "Applications of fractional gradient descent method with adaptive momentum in BP neural networks," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    3. Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Kiani, Adiqa Kausar & Raja, Muhammad Asif Zahoor & Chaudhary, Iqra Ishtiaq & Pinto, Carla M.A., 2022. "Design of auxiliary model based normalized fractional gradient algorithm for nonlinear output-error systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. Mei-Qi, Wang & Wen-Li, Ma & En-Li, Chen & Yu-Jian, Chang & Cui-Yan, Wang, 2022. "Principal resonance analysis of piecewise nonlinear oscillator with fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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