A Two-Dimensional Approach to Iterative Learning Control with Randomly Varying Trial Lengths

Abstract

In this paper, iterative learning control (ILC) is considered to solve the tracking problem of time-varying linear stochastic systems with randomly varying trial lengths. Using the two-dimensional Kalman filtering technique, the authors can establish a recursive framework for designing the learning gain matrix along both time and iteration axes by optimizing the trace of input error covariance matrix. It is strictly proved that the input error converges to zero asymptotically in mean square sense and thus the tracking error covariance converges. The extensions to that prior distribution of nonuniform trial lengths is unknown are also investigated with an asymptotical estimation method. Numerical simulations are provided to verify the effectiveness of the proposed framework.

This is a preview of subscription content, log in to check access.

References

  1. [1]

    Arimoto S, Kawamura S, and Miyazaki F, Bettering operation of robots by learning, Journal of Robotic Systems, 1984, 1(2), 123–140.

    Google Scholar 

  2. [2]

    Bristow D A, Tharayil M, and Alleyne A G, A survey of iterative learning control, IEEE Control Systems Magazine, 2006, 26(3), 96–114.

    Google Scholar 

  3. [3]

    Ahn H S, Chen Y Q, and Moore K L, Iterative learning control: brief survey and categorization, IEEE Transactions on Systems Man & Cybernetics Part C, 2007, 37(6), 1099–1121.

    Google Scholar 

  4. [4]

    Xu J X, A survey on iterative learning control for nonlinear systems, International Journal of Control, 2011, 84(7), 1275–1294.

    MathSciNet  MATH  Google Scholar 

  5. [5]

    Shen D and Wang Y, Survey on stochastic iterative learning control, Journal of Process Control, 2014, 24(12), 64–77.

    Google Scholar 

  6. [6]

    Shen D, Iterative learning control with incomplete information: A survey, IEEE/CAA Journal of Automatica Sinica, 2018, 5(5), 885–901.

    MathSciNet  Google Scholar 

  7. [7]

    Shen D, A technical overview of recent progresses on stochastic iterative learning control, Unmanned Systems, 2018, 6(3), 147–164.

    Google Scholar 

  8. [8]

    Li X, Ren Q, and Xu J X, Precise speed tracking control of a robotic fish via iterative learning control, IEEE Transactions on Industrial Electronics, 2016, 63(4), 2221–2228.

    Google Scholar 

  9. [9]

    Zeng C, Shen D, and Wang J, Adaptive learning tracking for robot manipulators with varying trial lengths, Journal of the Franklin Institute, 2019, 356(12), 5993–6014.

    MathSciNet  MATH  Google Scholar 

  10. [10]

    Shen D and Xu J X, Distributed learning consensus for heterogenous high-order nonlinear multi-agent systems with output constraints, Automatica, 2018, 97: 64–72.

    MathSciNet  MATH  Google Scholar 

  11. [11]

    Meng D, Jia Y, and Du J, Robust consensus tracking control for multiagent systems with initial state shifts, disturbances, and switching topologies, IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(4), 809–824.

    MathSciNet  Google Scholar 

  12. [12]

    Meng D, Jia Y, and Du J, Consensus seeking via iterative learning for multi-agent systems with switching topologies and communication time-delays, International Journal of Robust and Nonlinear Control, 2016, 26(17), 3772–3790.

    MathSciNet  MATH  Google Scholar 

  13. [13]

    Shen D and Xu Y, Iterative learning control for discrete-time stochastic systems with quantized information, IEEE/CAA Journal of Automatica Sinica, 2016, 3(1), 59–67.

    MathSciNet  Google Scholar 

  14. [14]

    Zhang C and Shen D, Zero-error convergence of iterative learning control based on uniform quantisation with encoding and decoding mechanism, IET Control Theory & Applications, 2018, 12(14), 1907–1915.

    MathSciNet  Google Scholar 

  15. [15]

    Bu X, Hou Z, Cui L, et al., Stability analysis of quantized iterative learning control systems using lifting representation, International Journal of Adaptive Control and Signal Processing, 2017, 31(9), 1327–1336.

    MathSciNet  MATH  Google Scholar 

  16. [16]

    Zhang T and Li J, Event-triggered iterative learning control for multi-agent systems with quantization, Asian Journal of Control, 2018, 20(3), 1088–1101.

    MathSciNet  MATH  Google Scholar 

  17. [17]

    Xiong W, Yu X, Patel R, et al., Iterative learning control for discrete-time systems with event-triggered transmission strategy and quantization, Automatica, 2016, 72: 84–91.

    MathSciNet  MATH  Google Scholar 

  18. [18]

    Shen D, Data-driven learning control for stochastic nonlinear systems: Multiple communication constraints and limited storage, IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(6), 2429–2440.

    MathSciNet  Google Scholar 

  19. [19]

    Shen D and Xu J X, A novel Markov chain based ILC analysis for linear stochastic systems under general data dropouts environments, IEEE Transactions on Automatic Control, 2017, 62(11): 5850–5857.

    MathSciNet  MATH  Google Scholar 

  20. [20]

    Li X, Xu J X, and Huang D, An iterative learning control approach for linear systems with randomly varying trial lengths, IEEE Transactions on Automatic Control, 2014, 59(7): 1954–1960.

    MathSciNet  MATH  Google Scholar 

  21. [21]

    Li X, Xu J X, and Huang D, Iterative learning control for nonlinear dynamic systems with randomly varying trial lengths, International Journal of Adaptive Control and Signal Processing, 2015, 29(11), 1341–1353.

    MathSciNet  MATH  Google Scholar 

  22. [22]

    Shen D, Zhang W, Wang Y, et al., On almost sure and mean square convergence of p-type ilc under randomly varying iteration lengths, Automatica, 2016, 63: 359–365.

    MathSciNet  MATH  Google Scholar 

  23. [23]

    Shen D, Zhang W, and Xu J X, Iterative learning control for discrete nonlinear systems with randomly iteration varying lengths, Systems & Control Letters, 2016, 96: 81–87.

    MathSciNet  MATH  Google Scholar 

  24. [24]

    Li X and Shen D, Two novel iterative learning control schemes for systems with randomly varying trial lengths, Systems & Control Letters, 2017, 107: 9–16.

    MathSciNet  MATH  Google Scholar 

  25. [25]

    Wei Y S and Li X D, Robust higher-order ILC for non-linear discrete-time systems with varying trial lengths and random initial state shifts, IET Control Theory & Applications, 2017, 11(15), 2440–2447.

    MathSciNet  Google Scholar 

  26. [26]

    Wang L, Li X, and Shen D, Sampled-data iterative learning control for continuous-time nonlinear systems with iteration-varying lengths, International Journal of Robust and Nonlinear Control, 2018, 28(8), 3073–3091.

    MathSciNet  MATH  Google Scholar 

  27. [27]

    Shen D and Xu J X, Adaptive learning control for nonlinear systems with randomly varying iteration lengths, IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(4), 1119–1132.

    MathSciNet  Google Scholar 

  28. [28]

    Zeng C, Shen D, and Wang J, Adaptive learning tracking for uncertain systems with partial structure information and varying trial lengths, Journal of the Franklin Institute, 2018, 355(15), 7027–7055.

    MathSciNet  MATH  Google Scholar 

  29. [29]

    Shen D and Xu J X, Robust learning control for nonlinear systems with nonparametric uncertainties and nonuniform trial lengths, International Journal of Robust and Nonlinear Control, 2019, 29(5), 1302–1324.

    MathSciNet  MATH  Google Scholar 

  30. [30]

    Saab S S, A discrete-time stochastic learning control algorithm, IEEE Transactions on Automatic Control, 2001, 46(6), 877–887.

    MathSciNet  MATH  Google Scholar 

  31. [31]

    Ahn H S, Chen Y Q, and Moore K L, Intermittent iterative learning control, IEEE International Symposium on Intelligent Control, Munich, 2006, 832–837.

    Google Scholar 

  32. [32]

    Ahn H S, Moore K L, and Chen Y Q, Discrete-time intermittent iterative learning controller with independent data dropouts, IFAC Proceedings Volumes, 2008, 41(2), 12442–12447.

    Google Scholar 

  33. [33]

    Roesser R P, A discrete state-space model for linear image processing, IEEE Transactions on Automatic Control, 1975, 20(1), 1–10.

    MathSciNet  MATH  Google Scholar 

  34. [34]

    Horn R A and Johnson C R, Matrix Analysis, Cambridge University Press, New York, 1985.

    Google Scholar 

  35. [35]

    Zhou W, Yu M, and Huang D, A high-order internal model based iterative learning control scheme for discrete linear time-varying systems, International Journal of Automation and Computing, 2015, 12(3), 330–336.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Dong Shen.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 61673045 and 11661016.

This paper was recommended for publication by Editor JIA Yingmin.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liu, C., Shen, D. & Wang, J. A Two-Dimensional Approach to Iterative Learning Control with Randomly Varying Trial Lengths. J Syst Sci Complex 33, 685–705 (2020). https://doi.org/10.1007/s11424-020-8215-z

Download citation

Keywords

  • Iterative learning control
  • Kalman filtering
  • recursive estimation
  • varying trial lengths