Stability analysis of continuous-time iterative learning control systems with multiple state delays

被引：2

作者：

Meng D.-Y. ^{[1
]}

Jia Y.-M. ^{[1
]}

Du J.-P. ^{[2
]}

Yu F.-S. ^{[3
]}

机构：

[1] The Seventh Research Division, Beihang University (BUAA)

[2] Beijing Key Laboratory of Intelligent Telecommunications Software and Multimedia, School of Computer Science and Technology, Beijing University of Posts and Telecommunications

[3] School of Electrical Engineering and Automation, Henan Polytechnic University

来源：

Zidonghua Xuebao/Acta Automatica Sinica | 2010年 / 36卷 / 05期

基金：

中国国家自然科学基金;

关键词：

2-D system theory; Iterative learning control (ILC); Linear matrix inequality (LMI); Monotonic convergence; Robust H[!sub]∞[!/sub] control theory; Time-delay systems;

D O I：

10.1016/s1874-1029(09)60030-6

中图分类号：

学科分类号：

摘要：

This paper presents a stability analysis of the iterative learning control (ILC) problem for continuous-time systems with multiple state delays, especially when system parameters are subject to polytopic-type uncertainties. Using the two-dimensional (2-D) analysis approach to ILC, the continuous-discrete Roesser's type linear systems are employed to describe the entire learning dynamics of time-delay systems (TDS) with the development of an expanding operator. Based on such Roesser systems, the 2-D system theory is first used to develop a necessary and sufficient condition for the asymptotic stability of ILC, and then the robust H∞ control theory is combined to provide a sufficient condition in terms of linear matrix inequalities (LMIs) for the monotonic convergence of ILC. It is shown that learning gains can be determined by solving LMIs, which ensure the control input error converges monotonically to zero as a function of iteration. Simulation results show that a robust asymptotically stable ILC scheme can become robustly monotonically convergent by adding the P-type learning gains that satisfy a set of LMIs, which can also improve the convergence rate greatly. Copyright © 2010 Acta Automatica Sinica. All rights reserved.

引用

页码：696 / 703

页数：7

共 19 条

[11]

Li X.D., Chow T.W.S., Ho J.K.L., Iterative learning control for a class of nonlinear discrete-time systems with multiple input delays, International Journal of Systems Science, 39, 4, pp. 361-369, (2008)

[12]

Meng D.Y., Jia Y.M., Du J.P., Yuan S., Feedback approach to design fast iterative learning controller for a class of time-delay systems, IET Control Theory and Applications, 3, 2, pp. 225-238, (2009)

[13]

Meng D.Y., Jia Y.M., Du J.P., Yu F.S., Robust design of a class of time-delay iterative learning control systems with initial shifts, IEEE Transactions on Circuits and Systems, Part I: Regular Papers, 56, 8, pp. 1744-1757, (2009)

[14]

Richard J.P., Time-delay systems: An overview of some recent advances and open problems, Automatica, 39, 10, pp. 1667-1694, (2003)

[15]

Geng Z., Carroll R., Xie J., Two-dimensional model and algorithm analysis for a class of iterative learning control systems, International Journal of Control, 52, 4, pp. 833-862, (1990)

[16]

Kurek J.E., Zaremba M.B., Iterative learning control synthesis based on 2-D system theory, IEEE Transactions on Automatic Control, 38, 1, pp. 121-125, (1993)

[17]

Saab S.S., A discrete-time learning control algorithm for a class of linear time-invariant systems, IEEE Transactions on Automatic Control, 40, 6, pp. 1138-1141, (1995)

[18]

Jia Y.-M., Control, (2007)

[19]

Sun M., Wang D., Iterative learning control with initial rectifying action, Automatica, 38, 7, pp. 1177-1182, (2002)

← 1 2 →