物理学报2011，Vol.60Issue(7)：129-136,8.
基于变分方法的混沌系统参数估计
Estimating parameters of chaotic system with variational method
摘要
Abstract
In this paper a method is presented to estimate the unknown parameters of chaotic system based on the variational principle, which can be applied to all chaotic systems governed by the following equation： X= F（x,θ）. Firstly, the equation of the chaotic system is included into the objective functional. Secondly, the universal formulas of the adjoint equation for chaotic systems and the functional gradient for unknown parameters are derived using the variational principle. Thirdly, the algorithm to estimate unknown parameters of chaotic system is designed according to above formulas. Finally, all unknown parameters of the typical Lorenz chaotic system and the hyperchaotic Chen system are estimated separately. Numerical simulations show that the effectiveness and the feasibility of the proposed method to estimate unknown parameters of chaotic systems.关键词
混沌系统/参数估计/变分方法/伴随方程Key words
chaotic system/parameter estimation/variational method/adjoint equation分类
数理科学引用本文复制引用
曹小群,宋君强,张卫民,赵军,张理论..基于变分方法的混沌系统参数估计[J].物理学报,2011,60(7):129-136,8.基金项目
国家自然科学基金（批准号：40775064,40505023）资助的课题. （）
