Article Contents
Article Contents

# 2-D analysis based iterative learning control for linear discrete-time systems with time delay

• This paper investigates an iterative learning controller for linear discrete-time systems with state delay based on two-dimensional (2-D) system theory. It shall be shown that a 2-D linear discrete Roessor's model can be applied to describe the ILC process of linear discrete time-delay systems. Much less restrictive conditions for the convergence of the proposed learning rules are derived. A learning algorithm is presented which provides much more effective learning of control input, which enables us to obtain a control input to drive the system output to the desired trajectory quickly. Numerical examples are included to illustrate the performance of the proposed control procedures.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

 Citation:

•  [1] S. Arimoto, S. Kawamura and F. Miyazaki, Bettering operation of robots by learning, J. Robot Syst., 1 (1984), 123-140.doi: 10.1002/rob.4620010203. [2] Y. Chen and Z. Gong, Analysis of a high-order iterative learning control algorithm for uncertain nonlinear systems with state delays, Automatica, 34 (1998), 345-353.doi: 10.1016/S0005-1098(97)00196-9. [3] J. Y. Choi and J. S. Lee, Adaptive iterative learning control of uncertain robotic systems, IEE, Proc. Contr. Theory Appl., 147 (2000), 217-223.doi: 10.1049/ip-cta:20000138. [4] T. W. S. Chow and Yong F, An iterative learning control method for continuous-time systems based on 2-D system theory, IEEE Trans. Circuits Syst., I Fundam. Theory Appl., 45 (1998), 683-689. [5] X. Fang, P. Chen and J. Shao, Optimal higher-order iterative learning control of discrete-time linear systems, IEE Pro.-Control Theory Appl., 152 (2005). [6] Y. Fang and T. W. S. Chow, 2-D Analysis for iterative learning control for discrete-time systems with variable initial conditions, IEEE Tran. Automat. Contr, 50 (2003). [7] Y. Fang and T. W. S. Chow, Iterative learning control of linear discrete-time multivariable system, Aoutmatica, 34 (1998), 1459-1462.doi: 10.1016/S0005-1098(98)00091-0. [8] K. Galkowski and E. Rogers, Stablility and dynamic boundary condition decoupling analysis for a class of 2-D dicrete linear systems, IEE Proc.-Circuits Devices Syst., 148 (2001). [9] Z. Geng, R. Carroll and J. Xies, Two-dimensional model and algorithm analysis for a class of iterative learning control system, Int. J. Contr., 52 (1990), 833-862.doi: 10.1080/00207179008953571. [10] Z. Geng and M. Jamshidi, Learning control system analysis and design based on 2-D system theory, J. Intell. Robot. Syst., (1990), 17-26.doi: 10.1007/BF00368970. [11] Feng-Hsiag. Hsiao and K. yeh, Robust D-stability analysis for discrete uncertain systems with multiple time delays, IEEE Tencon, (1993), 451-454. [12] D. H. Hwang, Z. Bien and S. R. Oh, Iterative learning control method for discrete-time dynamic systems, Proc. Inst. Elect. Eng. D, 138 (1991), 139-144. [13] T. Kaczorek, "Two-Dimensional Linear Systems," New York: Springer Verlag, 1985. [14] J. E. Kurek and M. B. Zaremba, Iterative learning control synthesis based on 2-D system theory, IEEE Trans. Automat. Contr., 38 (1993), 121-125.doi: 10.1109/9.186321. [15] X. D. Li and T. W. S Chow, 2-D System theory based iterative learning control for linear continuous system with time delay, IEEE Tran. Automat. Contr, 52 (2005). [16] X. D. Li and T. W. S Chow, Iterative learning control for linear time-variant discrete systems based on 2-D system theory, IEE Proc.-Control Theory Appl., 152 (2005). [17] K. L. Moore, "Iterative Learning Control for Deterministic Systems," New York: Springer-Verlag, 1993. [18] K. H. Park, Z. Bien and D. H. Hwang, Design of an iterative learning controller for a class of linear dynamic systems with time delay, IEE Proceedings-Control Theory and Applications, 145 (1998), 507-512.doi: 10.1049/ip-cta:19982409. [19] W. Paszke and K. Galkowsiki, Stability and stabilisation of 2D discrete linear systems with multiple delays, IEEE, 0-7803-7761, 2003. [20] T. Sugie and T. Ono, An iterative learning control law for dynamic systems, Automatica, 27 (1991), 729.doi: 10.1016/0005-1098(91)90066-B. [21] J. M. Xu and M. X. Sun, LMI_based robust iterative learning controller design for discrete linear uncertain systems, Journal of Control Theory and Application, 3 (2005), 259-265.doi: 10.1007/s11768-005-0046-x. [22] B. Zhang and G. Tang, PD-type iterative learning control for nonlinear time-delay system with external disturbance, Journal of System Engineering and Electronic, 17 (2006), 600-605.doi: 10.1016/S1004-4132(06)60103-5.