物理学报Issue(8)：1-11,11.DOI:10.7498/aps.62.080506
基于二阶离散变分方法的非线性映射参数估计
Parameter estimation of nonlinear map based on second-order discrete variational method∗
摘要
Abstract
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 Hyperhen´on 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.关键词
非线性映射/参数估计/二阶离散变分方法/伴随方程Key words
nonlinear map/parameter estimation/second-order discrete variational method/adjoint equation引用本文复制引用
曹小群†..基于二阶离散变分方法的非线性映射参数估计[J].物理学报,2013,(8):1-11,11.基金项目
国家重点基础研究发展计划(批准号:2009CB623605)、国家自然科学基金(批准号:21273030)、江苏省自然科学基金(批准号:BK2011408)、江苏省低维材料化学重点建设实验室开放课题(批准号:JSKC12109)和淮阴师范学院高级别科研项目培育基金(批准号:11HSGJBZ11)资助的课题.*Project supported by the National Basic Research Program of China (Grant No.2009CB623605), the National Natural Science Foundation of China (Grant No.21273030), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2011408), the Opening Project of Key Laboratory for Chemistry of Low-Dimensional Materials of Jiangsu Province, China (Grant No. JSKC12109), and the Cultivation Fund of the Key Scientific Innovation Project of Huaiyin Normal University, China (Grant No.11HSGJBZ11) （批准号:2009CB623605）
