4.7 Article

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

期刊

NONLINEAR DYNAMICS
卷 111, 期 16, 页码 15127-15144

出版社

SPRINGER
DOI: 10.1007/s11071-023-08623-3

关键词

Fractional chaotic system; Parameter estimation; Stepwise integration; Response sensitivity analysis; Trust-region constraint

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This paper presents a new parameter estimation approach for fractional chaotic systems based on stepwise integration and response sensitivity analysis. The approach includes three parts: obtaining the numerical solution of the Grunwald-Letnikov fractional-order equations through numerical discretization, proposing a new stepwise objective function with a unique minimum value, linearizing the nonlinear objective function to reduce solving difficulty, and introducing the trust-region constraint to improve convergence performance. The efficiency and viability of the approach are demonstrated through numerical tests.
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 Grunwald-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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