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Parameter estimation of fractional chaotic systems based on stepwise integration and response sensitivity analysis

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Abstract

This paper presents a new parameter estimation approach for fractional chaotic systems based on stepwise integration and response sensitivity analysis. This paper mainly consists of three parts. First, a numerical discretization scheme is introduced to obtain the numerical solution of the Grünwald–Letnikov fractional-order equations. Then, we propose a new stepwise objective function based on the single-step integration. Unlike the traditional nonlinear least-squares objective function with multiple local optimal values, the new objective function has a unique minimum value. Next, the nonlinear stepwise objective function is linearized to reduce the solving difficulty, and the trust-region constraint is introduced to raise the convergence performance of the proposed approach. Lastly, the efficiency and viability of the stepwise response sensitivity approach are demonstrated by several numerical tests.

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All data included in this study are available upon request by contact with the corresponding author.

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Acknowledgements

The present investigation was performed under the support of GuangDong Basic and Applied Basic Research Foundation (No. 2021A1515110750 and No. 2023A1515010028), Shenzhen Science and Technology Program (No. ZDSYS20210623091808026).

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The authors have not disclosed any funding.

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Shenzhen Campus of Sun Yat-sen University, Shenzhen, People’s Republic of China

    Tao Zhang, Zhong-rong Lu & Guang Liu

  2. Shenzhen Key Laboratory of Intelligent Microsatellite Constellation, Shenzhen, People’s Republic of China

    Tao Zhang & Guang Liu

  3. Sun Yat-sen University, Guangzhou, People’s Republic of China

    Ji-ke Liu

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  1. Tao Zhang
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  4. Guang Liu
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Contributions

TZ was involved in programming, formal analysis and writing the original draft. ZL took part in validation, supervision and funding acquisition. JL was responsible for programming and visualization. GL contributed to conceptualization, programming, visualization, methodology, investigation, writing—reviewing and editing, funding acquisition and project administration.

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Correspondence to Guang Liu.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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The MATLAB implementation codes in this paper can be downloaded at: Tao Zhang’s GitHub, Guang Liu’s Blog or Guang Liu’s Research Gate.

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Zhang, T., Lu, Zr., Liu, Jk. et al. Parameter estimation of fractional chaotic systems based on stepwise integration and response sensitivity analysis. Nonlinear Dyn 111, 15127–15144 (2023). https://doi.org/10.1007/s11071-023-08623-3

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