用移位Chebyshev正交多项式辨识非线性微分方程  

IDENTIFICATION OF THE NONLINEAR DIFFERENTIAL EQUATION WITH SHIFTED CHEBYSHEV POLYNOMIALS

作　　者：王孝红[1] 张峭滴 

机构地区：[1]山东建材学院 [2]淄博自来水公司

出　　处：《济南大学学报（自然科学版）》1990年第3期33-36,共4页Journal of University of Jinan(Science and Technology)

摘　　要：本文将移位Chebyshev正交多项式用于非线性微分方程的参数辨识中,给出移位Chebyshev向量的积分运算矩阵,将非线性微分方程转化为线性代数矩阵方程,用移位Chebyshev展开和最小二乘法估计方程的参数,本文给出计算实例。The shifted Chebyshev polynomial expansion is applied to identify the nonlinear differential equation. The integration matrix for the Chebyshev vector is derived so that the nonlinear differential equation is reduced to a linear matrix equation. In addition, parameter estimation of the nonlinear differential equation is presen ted also using shifted Chebyshev expansion and the least-squares method. The examples are given to demonstrate the accuray of this approach.

关 键 词：移位Chebyshev正交多项式 非线性微分方程 参数辨识 

分 类 号：N[自然科学总论]