American Institute of Mathematical Sciences

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January  2011, 7(1): 175-181. doi: 10.3934/jimo.2011.7.175

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

Chuandong Li 1, , Fali Ma 1, and  Tingwen Huang 2,

1. 

Department of Computer, Chongqing University, Chongqing 400044, China, China
2. 

Texas A&M University at Qatar, Doha, P.O.Box 5825

Received  December 2009 Revised  October 2010 Published  January 2011

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.
Keywords: 2-D system theory, Iterative learning control, time delay., linear discrete system.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Chuandong Li, Fali Ma, Tingwen Huang. 2-D analysis based iterative learning control for linear discrete-time systems with time delay. Journal of Industrial and Management Optimization, 2011, 7 (1) : 175-181. doi: 10.3934/jimo.2011.7.175
References:
[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.

show all references

References:
[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.

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