摘要
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.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2013年第8期42-52,共11页
Acta Physica Sinica
基金
国家自然科学基金(批准号:41105063)资助的课题~~
关键词
非线性映射
参数估计
二阶离散变分方法
伴随方程
nonlinear map
parameter estimation
second-order discrete variational method
adjoint equation
作者简介
通讯作者．E—mail：caoxiaoqun@nudt．edu．cn
