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一类不确定非线性系统的重复学习控制

李鹤 孙明轩 张静

李鹤, 孙明轩, 张静. 一类不确定非线性系统的重复学习控制. 自动化学报, 2018, 44(10): 1854-1863. doi: 10.16383/j.aas.2018.c160799
引用本文: 李鹤, 孙明轩, 张静. 一类不确定非线性系统的重复学习控制. 自动化学报, 2018, 44(10): 1854-1863. doi: 10.16383/j.aas.2018.c160799
LI He, SUN Ming-Xuan, ZHANG Jing. Repetitive Learning Control for a Class of Uncertain Nonlinear Systems. ACTA AUTOMATICA SINICA, 2018, 44(10): 1854-1863. doi: 10.16383/j.aas.2018.c160799
Citation: LI He, SUN Ming-Xuan, ZHANG Jing. Repetitive Learning Control for a Class of Uncertain Nonlinear Systems. ACTA AUTOMATICA SINICA, 2018, 44(10): 1854-1863. doi: 10.16383/j.aas.2018.c160799

一类不确定非线性系统的重复学习控制

doi: 10.16383/j.aas.2018.c160799
基金项目: 

国家自然科学基金 61573320

国家自然科学基金 61174034

国家自然科学基金 61374103

详细信息
    作者简介:

    李鹤  浙江工业大学信息工程学院博士研究生.主要研究方向为学习控制.E-mail:lihuoo@126.com

    张静  浙江工业大学信息工程学院硕士研究生.主要研究方向为学习控制.E-mail:zhangjingzjut@163.com

    通讯作者:

    孙明轩  浙江工业大学信息工程学院教授.主要研究方向为学习控制.本文通信作者.E-mail:mxsun@zjut.edu.cn

Repetitive Learning Control for a Class of Uncertain Nonlinear Systems

Funds: 

National Natural Science Foundation of China 61573320

National Natural Science Foundation of China 61174034

National Natural Science Foundation of China 61374103

More Information
    Author Bio:

     Ph. D. candidate at the College of Information Engineering, Zhejiang University of Technology. Her main research interest is learning control

     Master student at the College of Information Engineering, Zhejiang University of Technology. Her main research interest is learning control

    Corresponding author: SUN Ming-Xuan  Professor at the College of Information Engineering, Zhejiang University of Technology. His main research interest is learning control. Corresponding author of this paper
  • 摘要: 针对一类在有限时间区间上重复作业的不确定非线性系统,本文提出一种重复学习控制方法,用于解决非参数不确定性问题.该方法采用死区修正学习律对期望控制输入与界函数进行估计,以避免参数的正向累加导致系统发散,并使该控制算法较少地依赖于系统信息,更方便于控制器的实现.基于Lyapunov方法所设计的控制器,保证了闭环系统所有信号的有界性,并使得跟踪误差收敛于死区界定的邻域.通过仿真算例及电机实验结果验证所提学习控制算法的有效性.
    1)  本文责任编委 王聪
  • 图  1  误差性能指标$J_k$

    Fig.  1  Error performance index $J_k$

    图  2  第28次迭代的控制输入$u_k$

    Fig.  2  The control input $u_k$ at the 28th iteration

    图  3  参考输入估计$\hat u_k$

    Fig.  3  Estimate $\hat u_k$

    图  4  界函数估计$\hat l_{f, \, k}$

    Fig.  4  Estimate of the bound function $\hat l_{f, \, k}$

    图  5  界函数估计$\hat l_{g, \, k}$

    Fig.  5  Estimate of the bound function $\hat l_{g, \, k}$

    图  6  误差性能指标$J_k$

    Fig.  6  Error performance index $J_k$

    图  7  位置跟踪误差$e_1$

    Fig.  7  Position tracking error $e_1$

    图  8  控制输入$u_k$

    Fig.  8  Control input $u_k$

    图  9  参考输入的估计$\hat u_k$

    Fig.  9  Control input $\hat u_k$

    图  10  界函数估计$\hat l_{f, \, k}$

    Fig.  10  Estimate of the bound function $\hat l_{f, \, k}$

    图  11  界函数估计$\hat l_{g, \, k}$

    Fig.  11  Estimate of the bound function $\hat l_{g, \, k}$

    图  12  误差性能指标$J_k$ (其中三条虚线为控制器(31)的实验结果, 实线为控制器(11)的实验结果

    Fig.  12  Error performance index $J_k$ (the three dotted lines are the result by controller (31), the solid line is the result by controller (11))

    图  13  控制输入$u_k$ (其中三条虚线为控制器(31)的实验结果, 实线为控制器(11)的实验结果)

    Fig.  13  Control input $u_k$ (the three dotted lines are the result by controller (31), the solid line is the result by controller (11))

    图  14  参考输入的估计$\hat u_k$ (其中三条虚线为控制器(31)的实验结果, 实线为控制器(11)的实验结果)

    Fig.  14  Control input $\hat u_k$ (the three dotted lines are the result by controller (31), the solid line is the result by controller (11))

    图  15  误差性能指标$J_k$ (其中三条虚线为控制器(31)的实验结果, 实线为控制器(11)的实验结果)

    Fig.  15  Error performance index $J_k$ (the three dotted lines are the result by controller $ (31)$, the solid line is the result by controller $ (11)$)

    图  16  控制输入$u_k$ (其中三条虚线为控制器(31)的实验结果, 实线为控制器(11)的实验结果)

    Fig.  16  Control input $u_k$ (the three dotted lines are the result by controller (31), the solid line is the result by controller (11))

    图  17  参考输入的估计$\hat u_k$ (其中三条虚线为控制器(31)的实验结果, 实线为控制器(11)的实验结果)

    Fig.  17  Control input $\hat u_k$ (the three dotted lines are the result by controller (31), the solid line is the result by controller (11))

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出版历程
  • 收稿日期:  2016-12-04
  • 录用日期:  2017-08-17
  • 刊出日期:  2018-10-20

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