×

An accelerating iterative learning control based on an adjustable learning interval. (English) Zbl 1400.93103

Summary: An iterative learning control algorithm with an adjustable interval is proposed for nonlinear systems to accelerate the convergence rate of iterative learning control. For \(\lambda\)-norm, the monotonic convergence of ILC is analyzed, and the corresponding convergence conditions were obtained. The results showed that the convergence rate is mainly determined by the controlled object, the control law gain, the correction factor, and the iteration interval size and that the control law gain is corrected in real time in the modified interval and the modified interval shortened as the number of iterations increased, further accelerating the convergence. The numerical simulation shows the effectiveness of the proposed method.

MSC:

93C10 Nonlinear systems in control theory
68T05 Learning and adaptive systems in artificial intelligence
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Arimoto, S.; Kawamura, S.; Miyazaki, F., Bettering operation of Robots by learning, Journal of Robotic Systems, 1, 2, 123-140, (1984) · doi:10.1002/rob.4620010203
[2] Zsiga, N.; Van Dooren, S.; Elbert, P.; Onder, C. H., A new method for analysis and design of iterative learning control algorithms in the time-domain, Control Engineering Practice, 57, 39-49, (2016) · doi:10.1016/j.conengprac.2016.08.014
[3] Zhao, D.; Yang, Y., An iterative learning control design method for nonlinear discrete-time systems with unknown iteration-varying parameters and control direction, Mathematical Problems in Engineering, (2016) · Zbl 1400.93181 · doi:10.1155/2016/8971407
[4] Zhang, L.; Chen, W.; Liu, J.; Wen, C., A robust adaptive iterative learning control for trajectory tracking of permanent-magnet spherical actuator, IEEE Transactions on Industrial Electronics, 63, 1, 291-301, (2016) · doi:10.1109/TIE.2015.2464186
[5] Zhu, Q.; Xu, J.-X.; Huang, D.; Hu, G.-D., Iterative learning control design for linear discrete-time systems with multiple high-order internal models, Automatica. A Journal of IFAC, the International Federation of Automatic Control, 62, 65-76, (2015) · Zbl 1329.93095 · doi:10.1016/j.automatica.2015.09.017
[6] Yu, Q. X.; Hou, Z. S.; Chi, R. H., Adaptive iterative learning control for nonlinear uncertain systems with both state and input constraints, Journal of the Franklin Institute, 353, 15, 3920-3943, (2016) · Zbl 1347.93145 · doi:10.1016/j.jfranklin.2016.07.007
[7] Li, X.; Xu, J.-X.; Huang, D., Iterative learning control for nonlinear dynamic systems with randomly varying trial lengths, International Journal of Adaptive Control and Signal Processing, 29, 11, 1341-1353, (2015) · Zbl 1333.93274 · doi:10.1002/acs.2543
[8] Yan, L.; Wei, J., Fractional order nonlinear systems with delay in iterative learning control, Applied Mathematics and Computation, 257, 546-552, (2015) · Zbl 1338.93179 · doi:10.1016/j.amc.2015.01.014
[9] Kawamura, S.; Miyazaki, F.; Arimoto, S., Intelligent control of robot motion based on learning method, Memoirs of the Research Institute of Science and Engineering Ritumeikan University, 46, (1987)
[10] Arif, M.; Ishihara, T.; Inooka, H., Iterative learning control using information database (ILCID), Journal of Intelligent and Robotic Systems: Theory and Applications, 25, 1, 27-41, (1999) · Zbl 0945.93550 · doi:10.1023/A:1008004818981
[11] Yang, S.-Y.; Fan, X.-P.; Luo, A., Experience based acquisition of the initial value for the iterative learning control inputs, Kongzhi yu Juece/Control and Decision, 19, 1, 27-35, (2004)
[12] Wang, X.-S.; Peng, G.-Z.; Cheng, Y.-H., Iterative learning controller for manipulators based on the RBF network, Transaction of Beijing Institute of Technology, 24, 6, 512-515, (2004)
[13] Bien, Z.; Huk, K. M., Higher-order iterative control algorithm, IEEE Proceedings Part D: Control Theory and Applications, 136, 3, 105-112, (1989) · Zbl 0731.93047
[14] Lin, H.; Wang, L., Iterative Learning Control Theory, (1998), Xi’an, China: Northwestern Polytechnical University Press, Xi’an, China
[15] Piao, F. X.; Zhang, Q. L.; Wang, Z. F., Analysis of convergence rate for iterative learning control, Journal of Northeastern University, 27, 8, 835-838, (2006) · Zbl 1139.93362
[16] Xu, J.-X.; Tan, Y., Robust optimal design and convergence properties analysis of iterative learning control approaches, Automatica, 38, 11, 1867-1880, (2002) · Zbl 1011.93511 · doi:10.1016/s0005-1098(02)00143-7
[17] Ruan, X.-E.; Zhao, J.-Y., Pulse compensated iterative learning control to nonlinear systems with initial state uncertainty, Kongzhi Lilun Yu Yingyong/Control Theory and Applications, 29, 8, 993-1000, (2012) · Zbl 1274.93125
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.