时变切换信号驱动的线性连续切换系统的迭代学习控制收敛性分析

数学物理学报 ›› 2018, Vol. 38 ›› Issue (3): 599-612.

时变切换信号驱动的线性连续切换系统的迭代学习控制收敛性分析

杨轩¹, 阮小娥², 王彭³

1 西安工程大学理学院西安 710048;
2 西安交通大学数学与统计学院西安 710049;
3 中国人民解放军63771部队陕西渭南 714000

收稿日期:2017-04-06 修回日期:2017-10-16 出版日期:2018-06-26 发布日期:2018-06-26
通讯作者: 杨轩 E-mail:yangxuan@xpu.edu.cn
作者简介:阮小娥,E-mail:wruanxe@xjtu.edu.cn;王彭,E-mail:xajdwangpeng@126.com
基金资助:
西安工程大学博士基金（BS1617）

Convergence Analysis of Iterative Learning Control for Linear Continuous-Time Switched Systems with Arbitrary Time-Driven Switching Rules

Yang Xuan¹, Ruan Xiaoe², Wang Peng³

1 School of Science, Xi'an Polytechnic University, Xi'an 710048;
2 School of Mathematics and Statistics, Xian Jiaotong University, Xi'an 710049;
3 Troops 63771 of PLA, Shaanxi Weinan 714000

Received:2017-04-06 Revised:2017-10-16 Online:2018-06-26 Published:2018-06-26
Supported by:
Supported by the Doctoral Foundation of Xi'an Polytechnic University (BS1617)

摘要/Abstract

摘要： 针对一类由任意时变切换信号驱动并在某个时间区间可重复运行的切换系统，该文研究一阶和高阶PD-型迭代学习控算法.利用卷积积分的广义Young不等式，在Lebesgue-p范数意义下分析跟踪误差性态，得出算法收敛的充分条件，并量化了状态矩阵对学习效果的影响.数值仿真验证了理论结果的可行性和有效性.

关键词: 迭代学习控制, 切换系统, 切换律, Lebesgue-p范数, 广义Young不等式, 收敛性

Abstract: This paper addresses the convergence performance of first-order and higher-order PD-type iterative learning control strategies for a class of linear continuous-time switched systems. The manipulated systems are elaborated by arbitrary time-driven switching signals and can repetitively operate over a finite time interval. By employing the generalized Young inequality of convolution integral theoretical analysis is launched in the sense of Lebesgue-p norm. Simultaneously, sufficient convergence conditions of the algorithms are derived and the effect of the state matrices on the learning performance is quantized. To illustrate the validity and effectiveness of the theoretical results, numerical simulations are conducted.

Key words: Iterative learning control, Switched systems, Switching rules, Lebesgue-p norm, Generalized Young inequality, Convergence

中图分类号:

O231.1

杨轩, 阮小娥, 王彭. 时变切换信号驱动的线性连续切换系统的迭代学习控制收敛性分析[J]. 数学物理学报, 2018, 38(3): 599-612.

Yang Xuan, Ruan Xiaoe, Wang Peng. Convergence Analysis of Iterative Learning Control for Linear Continuous-Time Switched Systems with Arbitrary Time-Driven Switching Rules[J]. Acta mathematica scientia,Series A, 2018, 38(3): 599-612.

参考文献

[1] Chai T Y, Ding J L, Wang H, Su C Y. Hybrid intelligent optimal control method for operation of complex industrial processes. Acta Automatical Sinica, 2008, 34(5):505-515
[2] Zhang X, Xue D F, Wang J Y, Feng X Q. Improved growth technology of large MgO single crystals. Journal of Crystal Growth, 2006, 292(2):505-509
[3] Lin H, Antsaklis P J. Stability and stabilizability of switched linear systems:a survey of recent results. IEEE Transactions on Automatic Control, 2009, 54(2):308-322
[4] Zhao X, Yin S, Li H, et al. Switching stabilization for a class of slowly switched systems. IEEE Transactions on Automatic Control, 2015, 60(1):221-226
[5] Niu B, Zhao J. Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems. Systems and Control Letters, 2013, 62(10):963-971
[6] Lian J, Ge Y. Robust output tracking control for switched systems under asynchronous switching. Nonlinear Analysis:Hybrid Systems, 2013, 8:57-68
[7] Li Q K, Zhao J, Liu X J, et al. Observer-based tracking control for switched linear systems with timevarying delay. International Journal of Robust and Nonlinear Control, 2011, 21(3):309-327
[8] Hou L, Zong G, et al. Exponential l₁ -l_∞ output tracking control for discrete-time switched system with time-varying delay. International Journal of Robust and Nonlinear Control, 2012, 22(11):1175-1194
[9] Tong S, Zhang L, Li Y. Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead zones. IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2016, 46(1):37-47
[10] Niu B, Zhao J. Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function. International Journal of Systems Science, 2013, 44(5):978-985
[11] Zhao X, Shi P, Zheng X, et al. Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone. Automatica, 2015, 60:193-200
[12] Tharayil D A B, Alleyne A G. A survey of iterative learning control:a learning-based method for high performance tracking control. IEEE Control Systems Magazine, 2006, 26(3):96-114
[13] Ahn H S, Chen, Y Q, Koore K L. Iterative learning control:brief survey and categorization. IEEE Transactions on Systems Man and Cybernetics Part C Applications and Reviews, 2007, 37(6):1099-1121
[14] Ruan X, Bien Z Z, Wang Q. Convergence properties of iterative learning control processes in the sense of the Lebesgue-p norm. Asian Journal of Control, 2012, 14(4):1095-1107
[15] Bu X H, Hou Z S, Jin S T. An iterative learning control design approach for networked control systems with data dropouts. International Journal of Robust and Nonlinear Control, 2016, 26(1):91-109
[16] Yang X. A PD-Type iterative learning control for a class of switched discrete-time systems with model uncertainties and external noises. Discrete Dynamics in Nature and Society, 2015, Article ID:410292
[17] Bu X H, Yu F S, Hou Z S, et al. Iterative learning control for a class of linear discrete-time switched systems. Acta Automatica Sinica, 2013, 39(9):1564-1569
[18] Yang X, Ruan X. Analysis of iterative learning control for a class of linear discrete-time switched systems. Abstract and Applied Analysis, 2015, Article ID:464175
[19] Bu X, Hou Z, Yu F, Fu Z. Iterative learning control for a class of non-linear switched systems. IET Control Theory and Applications, 2013, 7(3):470-481
[20] Bu X, Yu F, Hou Z. Iterative learning control for linear switched systems with arbitrary switched rules. Intelligent Control and Automation (WCICA), 2012 World Congress on, 2012, DOI:10.1109/WCICA.2012. 6358060
[21] Bu X, Yu F, Fu Z, et al. Stability analysis of high-order iterative learning control for a class of nonlinear switched systems. Abstract and Applied Analysis, 2013, Article ID:684642
[22] Cao W, Sun M. Iterative learning control for discrete-time switched systems with attenuation factor. Journal of Vibration and Control, 2016, 22(12):2898-2906
[23] Shao Z, Xiang Z. Design of an iterative learning control law for a class of switched repetitive systems. Circuits, Systems, and Signal Processing, 2017, 36(2):845-866
[24] Wang J, Luo J, Hu Y. Monotonically convergent hybrid ILC for uncertain discrete-time switched systems with state delay. Transactions of the Institute of Measurement and Control, 2017, 39(7):1047-1058
[25] Pinsky M A. Introduction to Fourier Analysis and Wavelets. Providence, RI:American Mathematical Soc, 2009
[26] Ruan X, Bien Z Z. Pulse compensation for PD-type iterative learning control against initial state shift. International Journal of Systems Science, 2012, 43(11):2172-2184
[27] Yuan C, Wu C F, Wu, F. Hybrid control for switched linear systems with average dwell time. IEEE Transactions on Automatic Control, 2015, 60(1):240-245