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Nonlinear augmented Lagrangian for nonconvex multiobjective optimization
2D analysis based iterative learning control for linear discretetime systems with time delay
1.  Department of Computer, Chongqing University, Chongqing 400044, China, China 
2.  Texas A&M University at Qatar, Doha, P.O.Box 5825 
References:
[1] 
S. Arimoto, S. Kawamura and F. Miyazaki, Bettering operation of robots by learning, J. Robot Syst., 1 (1984), 123140. doi: 10.1002/rob.4620010203. 
[2] 
Y. Chen and Z. Gong, Analysis of a highorder iterative learning control algorithm for uncertain nonlinear systems with state delays, Automatica, 34 (1998), 345353. doi: 10.1016/S00051098(97)001969. 
[3] 
J. Y. Choi and J. S. Lee, Adaptive iterative learning control of uncertain robotic systems, IEE, Proc. Contr. Theory Appl., 147 (2000), 217223. doi: 10.1049/ipcta:20000138. 
[4] 
T. W. S. Chow and Yong F, An iterative learning control method for continuoustime systems based on 2D system theory, IEEE Trans. Circuits Syst., I Fundam. Theory Appl., 45 (1998), 683689. 
[5] 
X. Fang, P. Chen and J. Shao, Optimal higherorder iterative learning control of discretetime linear systems, IEE Pro.Control Theory Appl., 152 (2005). 
[6] 
Y. Fang and T. W. S. Chow, 2D Analysis for iterative learning control for discretetime systems with variable initial conditions, IEEE Tran. Automat. Contr, 50 (2003). 
[7] 
Y. Fang and T. W. S. Chow, Iterative learning control of linear discretetime multivariable system, Aoutmatica, 34 (1998), 14591462. doi: 10.1016/S00051098(98)000910. 
[8] 
K. Galkowski and E. Rogers, Stablility and dynamic boundary condition decoupling analysis for a class of 2D dicrete linear systems, IEE Proc.Circuits Devices Syst., 148 (2001). 
[9] 
Z. Geng, R. Carroll and J. Xies, Twodimensional model and algorithm analysis for a class of iterative learning control system, Int. J. Contr., 52 (1990), 833862. doi: 10.1080/00207179008953571. 
[10] 
Z. Geng and M. Jamshidi, Learning control system analysis and design based on 2D system theory, J. Intell. Robot. Syst., (1990), 1726. doi: 10.1007/BF00368970. 
[11] 
FengHsiag. Hsiao and K. yeh, Robust Dstability analysis for discrete uncertain systems with multiple time delays, IEEE Tencon, (1993), 451454. 
[12] 
D. H. Hwang, Z. Bien and S. R. Oh, Iterative learning control method for discretetime dynamic systems, Proc. Inst. Elect. Eng. D, 138 (1991), 139144. 
[13] 
T. Kaczorek, "TwoDimensional Linear Systems," New York: Springer Verlag, 1985. 
[14] 
J. E. Kurek and M. B. Zaremba, Iterative learning control synthesis based on 2D system theory, IEEE Trans. Automat. Contr., 38 (1993), 121125. doi: 10.1109/9.186321. 
[15] 
X. D. Li and T. W. S Chow, 2D 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 timevariant discrete systems based on 2D system theory, IEE Proc.Control Theory Appl., 152 (2005). 
[17] 
K. L. Moore, "Iterative Learning Control for Deterministic Systems," New York: SpringerVerlag, 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 ProceedingsControl Theory and Applications, 145 (1998), 507512. doi: 10.1049/ipcta:19982409. 
[19] 
W. Paszke and K. Galkowsiki, Stability and stabilisation of 2D discrete linear systems with multiple delays, IEEE, 078037761, 2003. 
[20] 
T. Sugie and T. Ono, An iterative learning control law for dynamic systems, Automatica, 27 (1991), 729. doi: 10.1016/00051098(91)90066B. 
[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), 259265. doi: 10.1007/s117680050046x. 
[22] 
B. Zhang and G. Tang, PDtype iterative learning control for nonlinear timedelay system with external disturbance, Journal of System Engineering and Electronic, 17 (2006), 600605. doi: 10.1016/S10044132(06)601035. 
show all references
References:
[1] 
S. Arimoto, S. Kawamura and F. Miyazaki, Bettering operation of robots by learning, J. Robot Syst., 1 (1984), 123140. doi: 10.1002/rob.4620010203. 
[2] 
Y. Chen and Z. Gong, Analysis of a highorder iterative learning control algorithm for uncertain nonlinear systems with state delays, Automatica, 34 (1998), 345353. doi: 10.1016/S00051098(97)001969. 
[3] 
J. Y. Choi and J. S. Lee, Adaptive iterative learning control of uncertain robotic systems, IEE, Proc. Contr. Theory Appl., 147 (2000), 217223. doi: 10.1049/ipcta:20000138. 
[4] 
T. W. S. Chow and Yong F, An iterative learning control method for continuoustime systems based on 2D system theory, IEEE Trans. Circuits Syst., I Fundam. Theory Appl., 45 (1998), 683689. 
[5] 
X. Fang, P. Chen and J. Shao, Optimal higherorder iterative learning control of discretetime linear systems, IEE Pro.Control Theory Appl., 152 (2005). 
[6] 
Y. Fang and T. W. S. Chow, 2D Analysis for iterative learning control for discretetime systems with variable initial conditions, IEEE Tran. Automat. Contr, 50 (2003). 
[7] 
Y. Fang and T. W. S. Chow, Iterative learning control of linear discretetime multivariable system, Aoutmatica, 34 (1998), 14591462. doi: 10.1016/S00051098(98)000910. 
[8] 
K. Galkowski and E. Rogers, Stablility and dynamic boundary condition decoupling analysis for a class of 2D dicrete linear systems, IEE Proc.Circuits Devices Syst., 148 (2001). 
[9] 
Z. Geng, R. Carroll and J. Xies, Twodimensional model and algorithm analysis for a class of iterative learning control system, Int. J. Contr., 52 (1990), 833862. doi: 10.1080/00207179008953571. 
[10] 
Z. Geng and M. Jamshidi, Learning control system analysis and design based on 2D system theory, J. Intell. Robot. Syst., (1990), 1726. doi: 10.1007/BF00368970. 
[11] 
FengHsiag. Hsiao and K. yeh, Robust Dstability analysis for discrete uncertain systems with multiple time delays, IEEE Tencon, (1993), 451454. 
[12] 
D. H. Hwang, Z. Bien and S. R. Oh, Iterative learning control method for discretetime dynamic systems, Proc. Inst. Elect. Eng. D, 138 (1991), 139144. 
[13] 
T. Kaczorek, "TwoDimensional Linear Systems," New York: Springer Verlag, 1985. 
[14] 
J. E. Kurek and M. B. Zaremba, Iterative learning control synthesis based on 2D system theory, IEEE Trans. Automat. Contr., 38 (1993), 121125. doi: 10.1109/9.186321. 
[15] 
X. D. Li and T. W. S Chow, 2D 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 timevariant discrete systems based on 2D system theory, IEE Proc.Control Theory Appl., 152 (2005). 
[17] 
K. L. Moore, "Iterative Learning Control for Deterministic Systems," New York: SpringerVerlag, 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 ProceedingsControl Theory and Applications, 145 (1998), 507512. doi: 10.1049/ipcta:19982409. 
[19] 
W. Paszke and K. Galkowsiki, Stability and stabilisation of 2D discrete linear systems with multiple delays, IEEE, 078037761, 2003. 
[20] 
T. Sugie and T. Ono, An iterative learning control law for dynamic systems, Automatica, 27 (1991), 729. doi: 10.1016/00051098(91)90066B. 
[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), 259265. doi: 10.1007/s117680050046x. 
[22] 
B. Zhang and G. Tang, PDtype iterative learning control for nonlinear timedelay system with external disturbance, Journal of System Engineering and Electronic, 17 (2006), 600605. doi: 10.1016/S10044132(06)601035. 
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