基于Haar小波运算矩阵的分数阶系统辨识方法

doi:10.16182/j.issn1004731x.joss.18-0703

系统仿真学报 ›› 2020, Vol. 32 ›› Issue (6): 1032-1037.doi: 10.16182/j.issn1004731x.joss.18-0703

基于Haar小波运算矩阵的分数阶系统辨识方法

李远禄^1,2, 李腾², 刘宝莹²

1. 南京信息工程大学自动化学院，江苏南京 210044;
2. 江苏省大气环境与装备技术协同创新中心，江苏南京 210044

收稿日期:2018-10-22 修回日期:2019-03-03 出版日期:2020-06-25 发布日期:2020-06-25
作者简介:李远禄(1973-)，男，湖南永兴，博士，教授，研究方向为分数阶系统、分数阶信号处理。
基金资助:
国家自然科学基金(61671010)，江苏省自然科学基金(BK20161535) ，江苏省高校“ 青蓝工程”(B2018Q03)

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

Li Yuanlu^1,2, Li Teng², Liu Baoying²

1. School of Automation, Nanjing University of Information Science & Technology, Nanjing 210044, China;
2. Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing University of Information Science & Technology, Nanjing 210044, China

Received:2018-10-22 Revised:2019-03-03 Online:2020-06-25 Published:2020-06-25

摘要/Abstract

摘要： 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。

关键词: 分数阶系统, Haar小波, 运算矩阵, 系统辨识

Abstract: 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.

Key words: fractional-order system, Haar wavelet, operational matrix, system identification

中图分类号:

N945.13

李远禄, 李腾, 刘宝莹. 基于Haar小波运算矩阵的分数阶系统辨识方法[J]. 系统仿真学报, 2020, 32(6): 1032-1037.

Li Yuanlu, Li Teng, Liu Baoying. Identification Method for Fractional-Order Systems Based on Haar Wavelet Operational Matrix[J]. Journal of System Simulation, 2020, 32(6): 1032-1037.

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基于Haar小波运算矩阵的分数阶系统辨识方法

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

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