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中国物理学会期刊

基于二阶离散变分方法的非线性映射参数估计

CSTR: 32037.14.aps.62.080506

Parameter estimation of nonlinear map based on second-order discrete variational method

CSTR: 32037.14.aps.62.080506
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  • 提出一种估计非线性映射未知参数的二阶离散变分方法.首先针对非线性离散混沌系统, 利用变分方法导出了伴随方程和目标泛函梯度, 以此为基础利用二阶离散变分方法给出了二阶伴随方程和精确计算Hessian矩阵-向量乘积的显式表达式; 其次设计了估计非线性映射未知参数的新算法, 并以此对Hyperhenón映射和二维抛物映射中的未知参数进行了精确的估计. 数值仿真结果表明了该方法的有效性和优点.

     

    In this paper a method is proposed to estimate the unknown parameters of nonlinear map based on the second-order discrete variational method. On the basis of adjoint equations and gradient expressions of cost functional derived from variational method, the second-order adjoint equations and the exact formulas for the Hessian-vector product are educed using the second-order discrete variational method. A new algorithm is given for estimating the unknown parameters of nonlinear maps. The numerical simulations show that all unknown physical parameters of Hyperhenón map and two-dimensional parabolic map are estimated successfully and precisely. Simulation results also demonstrate the validity and advantages of second-order discrete variational method of estimating the parameters of the discrete chaotic systems.

     

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