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.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Arimoto S, Kawamura S, and Miyazaki F, Bettering operation of robots by learning, Journal of Robotic Systems, 1984, 1(2), 123–140.
Bristow D A, Tharayil M, and Alleyne A G, A survey of iterative learning control, IEEE Control Systems Magazine, 2006, 26(3), 96–114.
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.
Xu J X, A survey on iterative learning control for nonlinear systems, International Journal of Control, 2011, 84(7), 1275–1294.
Shen D and Wang Y, Survey on stochastic iterative learning control, Journal of Process Control, 2014, 24(12), 64–77.
Shen D, Iterative learning control with incomplete information: A survey, IEEE/CAA Journal of Automatica Sinica, 2018, 5(5), 885–901.
Shen D, A technical overview of recent progresses on stochastic iterative learning control, Unmanned Systems, 2018, 6(3), 147–164.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Saab S S, A discrete-time stochastic learning control algorithm, IEEE Transactions on Automatic Control, 2001, 46(6), 877–887.
Ahn H S, Chen Y Q, and Moore K L, Intermittent iterative learning control, IEEE International Symposium on Intelligent Control, Munich, 2006, 832–837.
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.
Roesser R P, A discrete state-space model for linear image processing, IEEE Transactions on Automatic Control, 1975, 20(1), 1–10.
Horn R A and Johnson C R, Matrix Analysis, Cambridge University Press, New York, 1985.
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.
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.
About this article
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
- Iterative learning control
- Kalman filtering
- recursive estimation
- varying trial lengths