American Institute of Mathematical Sciences

Advanced
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 & 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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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). Google Scholar

[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). Google Scholar

[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.  Google Scholar

[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). Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[11]

Feng-Hsiag. Hsiao and K. yeh, Robust D-stability analysis for discrete uncertain systems with multiple time delays, IEEE Tencon, (1993), 451-454. Google Scholar

[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. Google Scholar

[13]

T. Kaczorek, "Two-Dimensional Linear Systems," New York: Springer Verlag, 1985. Google Scholar

[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.  Google Scholar

[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). Google Scholar

[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). Google Scholar

[17]

K. L. Moore, "Iterative Learning Control for Deterministic Systems," New York: Springer-Verlag, 1993. Google Scholar

[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.  Google Scholar

[19]

W. Paszke and K. Galkowsiki, Stability and stabilisation of 2D discrete linear systems with multiple delays, IEEE, 0-7803-7761, 2003. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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). Google Scholar

[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). Google Scholar

[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.  Google Scholar

[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). Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[11]

Feng-Hsiag. Hsiao and K. yeh, Robust D-stability analysis for discrete uncertain systems with multiple time delays, IEEE Tencon, (1993), 451-454. Google Scholar

[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. Google Scholar

[13]

T. Kaczorek, "Two-Dimensional Linear Systems," New York: Springer Verlag, 1985. Google Scholar

[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.  Google Scholar

[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). Google Scholar

[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). Google Scholar

[17]

K. L. Moore, "Iterative Learning Control for Deterministic Systems," New York: Springer-Verlag, 1993. Google Scholar

[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.  Google Scholar

[19]

W. Paszke and K. Galkowsiki, Stability and stabilisation of 2D discrete linear systems with multiple delays, IEEE, 0-7803-7761, 2003. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[1]

Meng Wang, Wendong Wang, Zhifei Zhang. On the uniqueness of weak solution for the 2-D Ericksen--Leslie system. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 919-941. doi: 10.3934/dcdsb.2016.21.919
[2]

Lingbing He. On the global smooth solution to 2-D fluid/particle system. Discrete & Continuous Dynamical Systems, 2010, 27 (1) : 237-263. doi: 10.3934/dcds.2010.27.237
[3]

H. T. Banks, R.C. Smith. Feedback control of noise in a 2-D nonlinear structural acoustics model. Discrete & Continuous Dynamical Systems, 1995, 1 (1) : 119-149. doi: 10.3934/dcds.1995.1.119
[4]

Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, 2021, 29 (4) : 2599-2618. doi: 10.3934/era.2021003
[5]

Roberto Triggiani. Stability enhancement of a 2-D linear Navier-Stokes channel flow by a 2-D, wall-normal boundary controller. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 279-314. doi: 10.3934/dcdsb.2007.8.279
[6]

Shaohong Fang, Jing Huang, Jinying Ma. Stabilization of a discrete-time system via nonlinear impulsive control. Discrete & Continuous Dynamical Systems - S, 2020, 13 (6) : 1803-1811. doi: 10.3934/dcdss.2020106
[7]

Jingang Zhao, Chi Zhang. Finite-horizon optimal control of discrete-time linear systems with completely unknown dynamics using Q-learning. Journal of Industrial & Management Optimization, 2021, 17 (3) : 1471-1483. doi: 10.3934/jimo.2020030
[8]

Melody Dodd, Jennifer L. Mueller. A real-time D-bar algorithm for 2-D electrical impedance tomography data. Inverse Problems & Imaging, 2014, 8 (4) : 1013-1031. doi: 10.3934/ipi.2014.8.1013
[9]

Zhixian Yu, Rong Yuan, Shaohua Gan. Novel entire solutions in a nonlocal 2-D discrete periodic media for bistable dynamics. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 4815-4838. doi: 10.3934/dcdsb.2020314
[10]

Antonio Pumariño, José Ángel Rodríguez, Enrique Vigil. Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors. Discrete & Continuous Dynamical Systems, 2018, 38 (2) : 941-966. doi: 10.3934/dcds.2018040
[11]

Shirshendu Chowdhury, Debanjana Mitra, Michael Renardy. Null controllability of the incompressible Stokes equations in a 2-D channel using normal boundary control. Evolution Equations & Control Theory, 2018, 7 (3) : 447-463. doi: 10.3934/eect.2018022
[12]

Bingbing Ding, Ingo Witt, Huicheng Yin. Blowup time and blowup mechanism of small data solutions to general 2-D quasilinear wave equations. Communications on Pure & Applied Analysis, 2017, 16 (3) : 719-744. doi: 10.3934/cpaa.2017035
[13]

Tian Ma, Shouhong Wang. Global structure of 2-D incompressible flows. Discrete & Continuous Dynamical Systems, 2001, 7 (2) : 431-445. doi: 10.3934/dcds.2001.7.431
[14]

Nusret Balci, Ciprian Foias, M. S Jolly, Ricardo Rosa. On universal relations in 2-D turbulence. Discrete & Continuous Dynamical Systems, 2010, 27 (4) : 1327-1351. doi: 10.3934/dcds.2010.27.1327
[15]

Jean-françois Coulombel, Paolo Secchi. Uniqueness of 2-D compressible vortex sheets. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1439-1450. doi: 10.3934/cpaa.2009.8.1439
[16]

Oleg Yu. Imanuvilov, Jean Pierre Puel. On global controllability of 2-D Burgers equation. Discrete & Continuous Dynamical Systems, 2009, 23 (1&2) : 299-313. doi: 10.3934/dcds.2009.23.299
[17]

Chao Deng, Tong Li. Global existence and large time behavior of a 2D Keller-Segel system in logarithmic Lebesgue spaces. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 183-195. doi: 10.3934/dcdsb.2018093
[18]

Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control & Related Fields, 2012, 2 (2) : 195-215. doi: 10.3934/mcrf.2012.2.195
[19]

Sie Long Kek, Mohd Ismail Abd Aziz, Kok Lay Teo, Rohanin Ahmad. An iterative algorithm based on model-reality differences for discrete-time nonlinear stochastic optimal control problems. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 109-125. doi: 10.3934/naco.2013.3.109
[20]

Alex Bombrun, Jean-Baptiste Pomet. Asymptotic behavior of time optimal orbital transfer for low thrust 2-body control system. Conference Publications, 2007, 2007 (Special) : 122-129. doi: 10.3934/proc.2007.2007.122

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (41)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences