基于Haar小波运算矩阵的分数阶系统辨识方法

分数阶微积分因为其阶数可以是任意数，因此能够更加准确的描述动态系统。虽然分数阶系统受到了越来越多的重视，可是，如何建立分数阶系统目前仍处于积极探究阶段。考虑到分数阶微分的非局部性，利用小波运算矩阵为工具，给出了一种分数阶系统的辨识方法。其好处在于能够利用小波的多分辨特性对激励信号和响应信号进行数据压缩，从而降低运算矩阵的维数，可解决因矩阵维数过大导致内存溢出的问题。

Identification Method for Fractional-Order Systems Based on Haar Wavelet Operational Matrix

Studies have shown that the dynamical systems can be more accurately described by the fractional-order systems because its order can be any number. That’s why the fractional-order systems are being paid more and more attention. However, how to create a fractional-order system is still in the exploratory stage. Considering the nonlocal features of the fractional differentiation, a method for the fractional-order system identification is proposed by taking the Haar wavelet operational matrix. The proposed method can reduce the dimension of the operational matrix by abandoning the high frequency coefficients of the input and output signals so that the buffer overflow problem of using the operational matrix to identify the systems can be solved.