物理学报
物理學報
물이학보
2013年
8期
080506-1-080506-11
,共1页
非线性映射%参数估计%二阶离散变分方法%伴随方程
非線性映射%參數估計%二階離散變分方法%伴隨方程
비선성영사%삼수고계%이계리산변분방법%반수방정
nonlinear map%parameter estimation%second-order discrete variational method%adjoint equation
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Hyperhen′on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.
提齣一種估計非線性映射未知參數的二階離散變分方法.首先針對非線性離散混沌繫統,利用變分方法導齣瞭伴隨方程和目標汎函梯度,以此為基礎利用二階離散變分方法給齣瞭二階伴隨方程和精確計算Hessian矩陣-嚮量乘積的顯式錶達式;其次設計瞭估計非線性映射未知參數的新算法,併以此對Hyperhen′on映射和二維拋物映射中的未知參數進行瞭精確的估計.數值倣真結果錶明瞭該方法的有效性和優點.
제출일충고계비선성영사미지삼수적이계리산변분방법.수선침대비선성리산혼돈계통,이용변분방법도출료반수방정화목표범함제도,이차위기출이용이계리산변분방법급출료이계반수방정화정학계산Hessian구진-향량승적적현식표체식;기차설계료고계비선성영사미지삼수적신산법,병이차대Hyperhen′on영사화이유포물영사중적미지삼수진행료정학적고계.수치방진결과표명료해방법적유효성화우점.
@@@@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.
