时变离散切换系统的迭代学习控制

曹伟; 孙明

doi:10.7498/aps.63.020201

摘要

针对一类具有任意切换序列的时变离散切换系统的轨迹跟踪问题，提出了一种离散迭代学习控制算法. 该算法在切换序列沿迭代轴不变而只沿时间轴变化的前提下，将整个有限时间区间划分为有限个子区间，并利用-范数对各个子区间上的收敛性进行了严格证明，给出了算法收敛的范数形式的充分条件. 该方法不仅实现了时变离散切换系统在有限时间内对目标轨迹的完全跟踪，而且结构简单更便于工程实现. 仿真结果验证了该方法的有效性.

关键词:

Aiming at the problem of trajectory tracking in a class of discrete time-varying switched system with arbitrary sequence, in this paper we propose a discrete iterative learning control algorithm. Under the precondition that the switched sequence does not change along the iterative axis but it does along the time axis, this algorithm divides the whole finite time region into several finite subintervals, and uses -norm to prove the convergence strictly, and provides the sufficient convergent condition of the algorithm in the norm form. This method not only realizes the complete tracking for a discrete time-varying switched system within a limited time, but also has a simple structure easy to be realized in engineering. Simulation results verify the validity of the method.

Keywords:

作者及机构信息

曹伟,
孙明

1.
齐齐哈尔大学计算机与控制工程学院, 齐齐哈尔 161006

基金项目: 国家自然科学基金青年科学基金（批准号：61100103）资助的课题.

Authors and contacts

Cao Wei,
Sun Ming

1.
College of Computer and Control Engineering, Qiqihar University, Qiqihar 161006, China

Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61100103).

参考文献

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[2]	Lin H, Antsaklis P J 2009 IEEE Trans. Autom. Control 54 308
[3]	Balluchi A, Dibenedett M D, Pinello C 1999 Automatica 35 519
[4]	Ooba T, Funahashi Y 2003 IEEE Trans. Autom. Control 42 1697
[5]	Gao C, Bi Q S, Zhang Z D 2013 Acta Phys. Sin. 62 020504 (in Chinese) [高超, 毕勤胜, 张正娣 2013 62 020504]
[6]	Wu L F, Guan Y, Liu Y 2013 Acta Phys. Sin. 62 110510 (in Chinese) [吴立峰, 关永, 刘勇 2013 62 110510]
[7]	Ma X D, Bi Q S 2013 Acta Phys. Sin. 61 240506 (in Chinese) [马新东, 毕勤胜 2013 61 240506]
[8]	Jia X C, Zheng L H, Chi X B 2009 Acta Autom. Sin. 35 1476 (in Chinese) [贾新春, 郑利红, 池小波 2009 自动化学报 35 1476]
[9]	Cheng D, Guo L, Lin Y 2005 IEEE Trans. Autom. Control 50 661
[10]	Lin H, Antsaklis P 2008 IEEE Trans. Autom. Control 53 1
[11]	Gao Z R, Shen Y X, Ji Z C 2012 Acta Phys. Sin. 61 120203 (in Chinese) [高在瑞, 沈艳霞, 纪志成 2012 61 120203]
[12]	Fang Z M, Xiang Z R, Chen Q W 2011 Control and Decision 26 1327 (in Chinese) [方志明, 向峥嵘, 陈庆伟 2011 控制与决策 26 1327]
[13]	Xiao H M, Zhao L, Wang C H 2011 Control Theory & Applications 28 1621 (in Chinese) [肖会敏, 赵林, 王春花 2011 控制理论与应用 28 1621]
[14]	Sharma R, Tewari A 2004 IEEE Trans. Control Syst. Technol. 12 677
[15]	No T S, Min B M, Stone R H 2005 Control Engineer. Pract. 13 601
[16]	Li L L, Shao C 2012 Control and Decision 27 304 (in Chinese) [李莉莉, 邵诚 2012 控制与决策 27 304]
[17]	Bu X H, Hou Z S, Yu F S 2012 Control Theory & Applications 29 1051 (in Chinese) [卜旭辉, 侯忠生, 余发山 2012 控制理论与应用 29 1051]
[18]	Arimoto S, Kawamura S, Miyazaki F 1984 J. Robo. Syst. 1 123
[19]	Cao W, Cong W, Li J 2012 Control and Decision 27 473 (in Chinese) [曹伟, 丛望, 李金 2012 控制与决策 27 473]
[20]	Chris T F, Cai Z L, Eric R, et al 2011 IEEE Trans. Control Syst. Technol. 19 590
[21]	Tian S P, Wu X S 2012 Control Theory & Applications 29 1082 (in Chinese) [田森平, 吴忻生 2012 控制理论与应用 29 1082]
[22]	Li Y, Chen Y Q, Ahn H S 2012 Control Theory & Applications 29 1031 (in Chinese) [李岩, 陈阳泉, 安孝晟 2012 控制理论与应用 29 1031]
[23]	Hou Z S, Xu J X, Yan J W 2008 Transport. Res. C 16 71
[24]	Gao F R, Yang Y, Shao C 2002 Chem. Engineer. Sci. 56 7025
[25]	Wang J, Hui G T, Xie X P 2013 Chin. Phys. B 22 030206
[26]	Wang J W, Zeng C B 2012 Chin. Phys. B 21 110206
[27]	Yin S, Luo H, Ding S 2013 IEEE Trans. Industrial Electron. 10.1109/TIE.2013.2273477
[28]	Yin S, Ding S X, Haghani A 2012 J. Process Control 22 1567

施引文献

[1]	Liberzon D, Morse A S 1999 IEEE Control Syst. Magazine 19 59
[2]	Lin H, Antsaklis P J 2009 IEEE Trans. Autom. Control 54 308
[3]	Balluchi A, Dibenedett M D, Pinello C 1999 Automatica 35 519
[4]	Ooba T, Funahashi Y 2003 IEEE Trans. Autom. Control 42 1697
[5]	Gao C, Bi Q S, Zhang Z D 2013 Acta Phys. Sin. 62 020504 (in Chinese) [高超, 毕勤胜, 张正娣 2013 62 020504]
[6]	Wu L F, Guan Y, Liu Y 2013 Acta Phys. Sin. 62 110510 (in Chinese) [吴立峰, 关永, 刘勇 2013 62 110510]
[7]	Ma X D, Bi Q S 2013 Acta Phys. Sin. 61 240506 (in Chinese) [马新东, 毕勤胜 2013 61 240506]
[8]	Jia X C, Zheng L H, Chi X B 2009 Acta Autom. Sin. 35 1476 (in Chinese) [贾新春, 郑利红, 池小波 2009 自动化学报 35 1476]
[9]	Cheng D, Guo L, Lin Y 2005 IEEE Trans. Autom. Control 50 661
[10]	Lin H, Antsaklis P 2008 IEEE Trans. Autom. Control 53 1
[11]	Gao Z R, Shen Y X, Ji Z C 2012 Acta Phys. Sin. 61 120203 (in Chinese) [高在瑞, 沈艳霞, 纪志成 2012 61 120203]
[12]	Fang Z M, Xiang Z R, Chen Q W 2011 Control and Decision 26 1327 (in Chinese) [方志明, 向峥嵘, 陈庆伟 2011 控制与决策 26 1327]
[13]	Xiao H M, Zhao L, Wang C H 2011 Control Theory & Applications 28 1621 (in Chinese) [肖会敏, 赵林, 王春花 2011 控制理论与应用 28 1621]
[14]	Sharma R, Tewari A 2004 IEEE Trans. Control Syst. Technol. 12 677
[15]	No T S, Min B M, Stone R H 2005 Control Engineer. Pract. 13 601
[16]	Li L L, Shao C 2012 Control and Decision 27 304 (in Chinese) [李莉莉, 邵诚 2012 控制与决策 27 304]
[17]	Bu X H, Hou Z S, Yu F S 2012 Control Theory & Applications 29 1051 (in Chinese) [卜旭辉, 侯忠生, 余发山 2012 控制理论与应用 29 1051]
[18]	Arimoto S, Kawamura S, Miyazaki F 1984 J. Robo. Syst. 1 123
[19]	Cao W, Cong W, Li J 2012 Control and Decision 27 473 (in Chinese) [曹伟, 丛望, 李金 2012 控制与决策 27 473]
[20]	Chris T F, Cai Z L, Eric R, et al 2011 IEEE Trans. Control Syst. Technol. 19 590
[21]	Tian S P, Wu X S 2012 Control Theory & Applications 29 1082 (in Chinese) [田森平, 吴忻生 2012 控制理论与应用 29 1082]
[22]	Li Y, Chen Y Q, Ahn H S 2012 Control Theory & Applications 29 1031 (in Chinese) [李岩, 陈阳泉, 安孝晟 2012 控制理论与应用 29 1031]
[23]	Hou Z S, Xu J X, Yan J W 2008 Transport. Res. C 16 71
[24]	Gao F R, Yang Y, Shao C 2002 Chem. Engineer. Sci. 56 7025
[25]	Wang J, Hui G T, Xie X P 2013 Chin. Phys. B 22 030206
[26]	Wang J W, Zeng C B 2012 Chin. Phys. B 21 110206
[27]	Yin S, Luo H, Ding S 2013 IEEE Trans. Industrial Electron. 10.1109/TIE.2013.2273477
[28]	Yin S, Ding S X, Haghani A 2012 J. Process Control 22 1567

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