非线性参数化时变时滞系统自适应迭代学习控制

数学物理学报 ›› 2011, Vol. 31 ›› Issue (3): 682-690.

非线性参数化时变时滞系统自适应迭代学习控制

李俊民

西安电子科技大学理学院西安 710071

收稿日期:2009-10-08 修回日期:2010-09-29 出版日期:2011-06-25 发布日期:2011-06-25
基金资助:
国家自然科学基金(60974139)和中央高校基本科研业务费专项资金资助

Adaptive Iterative Learning Control for Nonlinearly Parameterized Systems with Time-Varying Delays

LI Jun-Min

School of Science, Xidian University, Xi'an 710071

Received:2009-10-08 Revised:2010-09-29 Online:2011-06-25 Published:2011-06-25
Supported by:
国家自然科学基金(60974139)和中央高校基本科研业务费专项资金资助

摘要/Abstract

摘要：

针对含有未知时变参数和时变时滞的非线性参数化系统, 提出了一种新的自适应迭代学习控制方法. 该方法将参数分离技术与信号置换思想相结合, 可以处理含有时变参数和时滞不确定性的非线性系统. 设计了一种自适应控制策略, 使跟踪误差的平方在一个有限区间上的积分渐近收敛于零. 通过构造Lyapunov-Krasovskii型复合能量函数, 给出了闭环系统收敛的一个充分条件. 给出仿真例子验证了控制方法的有效性.

关键词: 非线性参数化系统, 自适应迭代学习控制, 时变参数;时变时滞, 复合能量函数

Abstract:

A new adaptive iterative learning control approach is proposed in this paper for a class of nonlinear systems with unknown time-varying parameters and time-varying delays. By using the parameter separation technique combined with the signal replacement mechanism, the approach can be applied to nonlinear systems with time-varying parameters and delay uncertainty. A novel adaptive control strategy is designed to ensure the tracking error converging to zero in the mean-square sense on the finite interval. A sufficient condition for the convergence is also given by constructing a Lyapunov-Krasovskii-like composite energy function. A simulation example is provided to illustrate the effectiveness of control algorithms proposed in this paper.

Key words: Nonlinearly parameterized systems, Adaptive iterative learning control, Time-varying parameters, Time-varying delays, Composite
energy function

中图分类号:

93C40

李俊民. 非线性参数化时变时滞系统自适应迭代学习控制[J]. 数学物理学报, 2011, 31(3): 682-690.

LI Jun-Min. Adaptive Iterative Learning Control for Nonlinearly Parameterized Systems with Time-Varying Delays[J]. Acta mathematica scientia,Series A, 2011, 31(3): 682-690.

参考文献

[1] Fu K S, Walts M. Aheuristic approach to reinforcement learning control system. IEEE Transactions on Automatic Control, 1965, 10: 390--398

[2] Arimoto S, Kawamura S, Miyazaki F. Bettering operation of robots by learning. Journal of Robotic Systems, 1984, 1: 123--140

[3] Moore K L. Iterative Learning Control for Deterministic Systems. London: Springer-Verlag, 1993

[4] Fang Y, Chow T W S. Iterative learning control of linear discrete-time multivariable systems. Automatica, 1998, 34: 1458--1464

[5] Deluca A, Stefano P. An iterative scheme for learning control gravity compensation in flexible robot arms. Automatica, 1994, 30: 993--1002

[6] Chen Y, Gong Z, Wen C. Analysis of a high-order iterative learning control algorithm for tracking control of delayed repeated systems.
Automatica, 1998, 34: 345--353

[7] Kuc T Y, Han W G. An adaptive PID learning control of robot manipulators. Automatica, 2000, 36: 717--725

[8] Chen H F, Fang H T. Output tracking for nonlinear stochastic systems by iterative learning control. IEEE Transactions on Automatica Control, 2004, 49: 583--588

[9] Choi J Y, Lee J S. Adaptive iterative learning control of uncertain robotic systems. IEE Proceedings-Control Theory and Applications, 2000, 147: 217--223

[10] Park B H, Kuc T Y, Lee J S. Adaptive learning control of uncertain robotic systems. International Journal of Control, 1996, 65: 725--744

[11] 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), 2004, 33: 589--597

[12] Xu J X, Qu Z H. Rubust iterative learning control for a class of nonlinear systems. Automatica, 1998, 34: 983--988

[13] 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: 1940--1945

[14] 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: 100--104

[15] 孙明轩, 黄宝健, 张学智.任意初态下不确定时滞系统的PD型迭代学习控制. 控制理论与应用, 1998, 15: 853--858

[16] Wu H. Design of iterative learning controllers for linear discrete systems with multiple time delays. IEEE Transactions on Electronics, Information and Systems, 2006, 126: 1138--1143

[17] Park K H, Bien Z, Hwang D H. Design of an iterative learning controller for a class of linear dynamic systems with time delay. IEE Proceedings-Control Theory and Applications, 1998, 145: 507--512

[18] Li X D, Chow T W S, Ho J K L. 2-D system theory based iterative learning control for linear continuous systems with time delays. IEEE Transactions on Circuits and Systems: I, 2005, 52: 1421--1430

[19] 方忠, 韩正之, 陈彭年. 一类时滞非线性系统的采样迭代学习控制.系统科学与数学, 2004, 24: 564--570

[20] Niculescu S I. Delay Effects on Stability: a Robust Control Approach. London: Springer-Verlag, 2001

[21] Narenda K S, Oleng N. Exact output tracking in decentralized adaptive control systems. IEEE Transactions on Automatic Control, 2002, 47: 390--395

[22] Lin W, Qian C. Adaptive control of nonlinearly parameterized systems: the smooth feedback case. IEEE Transactions on Automatic Control, 2002, 47: 1249--1266

[23] 张瑜, 孙继涛. 脉冲耦合时滞微分与连续差分系统的稳定性.数学物理学报, 2010, 30A(3): 694--70