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

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.