基于小波逼近变换的非线性分布参数系统辨识

利用Haar小波正交规范基的微分运算矩阵及其运算性质,将描述一类非线性分布参数系统的偏微分方程转化为代数矩阵方程,结合最小二乘法,确定出待辨识的系统参数,避免了对偏微分方程进行多重积分运算的繁琐;并且,可以不考虑初始条件和边界条件,较其他采用积分运算矩阵的辨识方法要简单得多,简化了分布参数系统辨识的求解过程。该方法简单,计算量小,辨识精度高。仿真结果表明了该算法应用在非线性分布参数系统辨识中的有效性。

Identification of Non-linear Distributed Parameter Systems Based on Wavelet Approximation Transform

The differential operational matrix of Haar wavelets and its properties are applied to the identification problem of a class of the non-linear distributed parameter systems(DPS).The partial differential equation describing non-linear DPS is transformed into an algebraic matrix equation.By using the least square parameter estimation algorithm,the identification is made,and the initial conditions and boundary conditions are not needed to consider.The proposed method is simpler than others which make use of the integrated operational matrix.The simulation results show the efficiency of the proposed method applying to non-linear distributed parameter system identification.