一类不确定系统的重复学习控制方法

管海娃; 孙明轩

doi:10.16383/j.aas.c180350

一类不确定系统的重复学习控制方法

doi: 10.16383/j.aas.c180350

管海娃^1,2,,
孙明轩^1, ,

1.
浙江工业大学信息工程学院杭州 310023
2.
温州科技职业学院温州 325006

基金项目:

国家自然科学基金 61174034

国家自然科学基金 61573320

详细信息

作者简介:
管海娃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: guanhaiwa1026@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

计量
- 文章访问数: 2038
- HTML全文浏览量: 612
- PDF下载量: 312
- 被引次数: 0
出版历程
- 收稿日期: 2018-05-26
- 录用日期: 2018-09-10
- 刊出日期: 2020-01-21

Repetitive Learning Control Method for a Class of Uncertain Systems

GUAN Hai-Wa^{1,2
,},
SUN Ming-Xuan^{1
, ,}

1.
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023
2.
Wenzhou Vocational College of Science and Technology, Wenzhou 325006

Funds:

National Natural Science Foundation of China 61174034

National Natural Science Foundation of China 61573320

More Information

Author Bio:
GUAN Hai-Wa Ph. D. candidate 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

摘要: 针对一类不确定非线性系统, 结合Backstepping方法, 设计重复学习控制方法.采用Lyapunov-like综合, 设计重复学习控制器处理系统中的参数和非参数不确定性, 可实现系统状态在整个作业区间上完全跟踪期望轨迹.分别讨论部分限幅和完全限幅学习机制, 证明闭环系统中各变量的一致有界性以及跟踪误差的一致收敛性.仿真结果验证了所提出控制方法的有效性.
- 重复学习控制 /
- 参数化 /
- 非参数化 /
- 不确定系统
Abstract: This paper presents a repetitive learning control approach for a class of uncertain nonlinear systems by means of the backstepping method. Based on Lyapunov-like synthesis, a learning controller is designed for handling parametric and nonparametric uncertainties, such that system state can completely track the reference trajectory over the whole time interval after many iterations. Both the partially-saturated and fully-saturated learning mechanisms are discussed respectively. The uniform boundedness of all variables in the closed-loop system and the uniform convergence of the tracking error are guaranteed. Simulation results demonstrate the effectiveness of the method.
- Repetitive learning control /
- parametrization /
- nonparametrization /
- uncertain systems
Recommended by Associate Editor HOU Zhong-Sheng
注释:

1) 本文责任编委侯忠生

HTML全文

图 1 $x_{1}$及参考轨迹$r_{1}$

Fig. 1 $x_{1}$ and the reference trajectory $r_{1}$

下载: 全尺寸图片幻灯片

图 2 $x_{2}$及参考轨迹$r_{2}$

Fig. 2 $x_{2}$ and the reference trajectory $r_{2}$

下载: 全尺寸图片幻灯片

图 3 变量$z_{1}$

Fig. 3 The variable $z_{1}$

下载: 全尺寸图片幻灯片

图 4 变量$z_{2}$

Fig. 4 The variable $z_{2}$

下载: 全尺寸图片幻灯片

图 5 控制输入$u$

Fig. 5 The control input $u$

下载: 全尺寸图片幻灯片

图 6 指标$J_{1, k}$

Fig. 6 The index $J_{1, k}$

下载: 全尺寸图片幻灯片

图 7 指标$J_{2, k}$

Fig. 7 The index $J_{2, k}$

下载: 全尺寸图片幻灯片

参考文献(21)

[1]	Arimoto S, Kawamura S, Miyazaki F. Bettering operation of robots by learning. Journal of Robotic Systems, 1984, 1(2): 123-140 doi: 10.1002/rob.4620010203
[2]	French M, Rogers E. Non-linear iterative learning by an adaptive Lyapunov technique. International Journal of Control, 2000, 73(10): 840-850 doi: 10.1080/002071700405824
[3]	Qu Z H, Xu J X. Asymptotic learning control for a class of cascaded nonlinear uncertain systems. IEEE Transactions on Automatic Control, 2002, 47(8): 1369-1376 doi: 10.1109/TAC.2002.801194
[4]	Xu J X, Tan Y. A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties. IEEE Transactions on Automatic Control, 2002, 47(11): 1940-1945 doi: 10.1109/TAC.2002.804460
[5]	Tayebi A, Chien C J. A unified adaptive iterative learning control framework for uncertain nonlinear systems. IEEE Transactions on Automatic Control, 2007, 52(10): 1907-1913 doi: 10.1109/TAC.2007.906215
[6]	Xu J X, Xu J. On iterative learning from different tracking tasks in the presence of time-varying uncertainties. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2004, 34(1): 589-597 doi: 10.1109/TSMCB.2003.818433
[7]	Chi R H, Sui S L, Hou Z S. A new discrete-time adaptive ILC for nonlinear systems with time-varying parametric uncertainties. Acta Automatica Sinica, 2008, 34(7): 805-808 https://www.sciencedirect.com/science/article/abs/pii/S1874102908600427#!
[8]	孙明轩, 严求真.迭代学习控制系统的误差跟踪设计方法.自动化学报, 2013, 39(3): 251-262 doi: 10.3724/SP.J.1004.2013.00251 Sun Ming-Xuan, Yan Qiu-Zhen. Error tracking of iterative learning control systems. Acta Automatica Sinica, 2013, 39(3): 251-262 doi: 10.3724/SP.J.1004.2013.00251
[9]	李俊民, 孙云平, 刘赟.非一致目标跟踪的混合自适应迭代学习控制.控制理论与应用, 2008, 25(1): 100-104 http://d.old.wanfangdata.com.cn/Periodical/kzllyyy200801018 Li Jun-Min, Sun Yun-Ping, Liu Yun. Hybrid adaptive iterative learning control of non-uniform trajectory tracking. Control Theory & Applications, 2008, 25(1): 100-104 http://d.old.wanfangdata.com.cn/Periodical/kzllyyy200801018
[10]	Dixon W E, Zergeroglu E, Dawson D M, Costic B T. Repetitive learning control: a Lyapunov-based approach. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2002, 32(4): 538-545 doi: 10.1109/TSMCB.2002.1018772
[11]	孙明轩, 王郸维, 陈彭年.有限区间非线性系统的重复学习控制.中国科学:信息科学, 2010, 40(3): 433-444 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zgkx-fc201003006 Sun Ming-Xuan, Wang Dan-Wei, Chen Peng-Nian. Repetitive learning control of nonlinear systems over finite intervals. Science in China Series F: Information Sciences, 2010, 53(1): 115-128 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zgkx-fc201003006
[12]	Choi J Y, Lee J S. Adaptive iterative learning control of uncertain robotic systems. IEE Proceedings-Control Theory and Application, 2000, 147(2): 217-223 doi: 10.1049/ip-cta:20000138
[13]	吕庆.抑制初态误差影响的自适应迭代学习控制.自动化学报, 2015, 41(7): 1365-1372 doi: 10.16383/j.aas.2015.c140670 Lv Qing. Adaptive iterative learning control for inhibition effect of initial state random error. Acta Automatica Sinica, 2015, 41(7): 1365-1372 doi: 10.16383/j.aas.2015.c140670
[14]	Yang Z Y, Yam S C P, Li L K, Wang Y W. Universal repetitive learning control for nonparametric uncertainty and unknown state-dependent control direction matrix. IEEE Transactions on Automatic Control, 2010, 55(7): 1710-1715 doi: 10.1109/TAC.2010.2046935
[15]	Jin X, Huang D Q, Xu J X. Iterative learning control for systems with nonparametric uncertainties under alignment condition. In: Proceedings of the 51st Conference on Decision and Control. Hawaii, USA: IEEE, 2012. 3942-3947
[16]	Yu M, Huang D Q, He W. Robust adaptive iterative learning control for discrete-time nonlinear systems with both parametric and nonparametric uncertainties. International Journal of Adaptive Control and Signal Processing, 2016, 30(7): 972-985 doi: 10.1002/acs.2648
[17]	Jin X, Xu J X. Iterative learning control for output-constrained systems with both parametric and nonparametric uncertainties. Automatica, 2013, 49(8): 2508-2516 doi: 10.1016/j.automatica.2013.04.039
[18]	齐丽强, 孙明轩, 管海娃.非参数不确定系统的有限时间迭代学习控制.自动化学报, 2014, 40(7): 1320-1327 doi: 10.3724/SP.J.1004.2014.01320 Qi Li-Qiang, Sun Ming-Xuan, Guan Hai-Wa. Finite-time iterative learning control for systems with nonparametric uncertainties. Acta Automatica Sinica, 2014, 40(7): 1320-1327 doi: 10.3724/SP.J.1004.2014.01320
[19]	余琼霞, 侯忠生.非参数不确定系统的自适应迭代学习控制.系统科学与数学, 2016, 36(1): 1-13 http://d.old.wanfangdata.com.cn/Periodical/zdhxb200807012 Yu Qiong-Xia, Hou Zhong-Sheng. Adaptive iterative learning control for a class of non-parametric uncertain systems. Journal of Systems Science and Mathematical Sciences, 2016, 36(1): 1-13 http://d.old.wanfangdata.com.cn/Periodical/zdhxb200807012
[20]	严求真, 孙明轩, 蔡建平.迭代学习控制的参考信号初始修正方法.自动化学报, 2017, 43(8): 1470-1477 doi: 10.16383/j.aas.2017.c160292 Yan Qiu-Zhen, Sun Ming-Xuan, Cai Jian-Ping. Reference-signal rectifying method of iterative learning control. Acta Automatica Sinica, 2017, 43(8): 1470-1477 doi: 10.16383/j.aas.2017.c160292
[21]	孙明轩.有限时间迭代学习控制.系统科学与数学, 2010, 30(6): 733-741 http://d.old.wanfangdata.com.cn/Periodical/xtkxysx-zw201006002 Sun Ming-Xuan. Finite-time iterative learning control. Journal of Systems Science and Mathematical Sciences, 2010, 30(6): 733-741 http://d.old.wanfangdata.com.cn/Periodical/xtkxysx-zw201006002

施引文献

资源附件(0)

访问统计

点击查看大图

图(7)

计量

文章访问数: 2038
HTML全文浏览量: 612
PDF下载量: 312
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

一类不确定系统的重复学习控制方法

doi: 10.16383/j.aas.c180350

作者简介:
管海娃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: guanhaiwa1026@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

计量

Repetitive Learning Control Method for a Class of Uncertain Systems

Author Bio:
GUAN Hai-Wa Ph. D. candidate 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.)

计量

目录

留言板

一类不确定系统的重复学习控制方法

doi: 10.16383/j.aas.c180350

作者简介: 管海娃 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: guanhaiwa1026@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

计量

出版历程

Repetitive Learning Control Method for a Class of Uncertain Systems

Author Bio: GUAN Hai-Wa Ph. D. candidate 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.)

计量

出版历程

目录

作者简介:
管海娃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: guanhaiwa1026@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

Author Bio:
GUAN Hai-Wa Ph. D. candidate at the College of Information Engineering, Zhejiang University of Technology. Her main research interest is learning control.)