zbMATH — the first resource for mathematics

Stability and robustness analysis of cyclic pseudo-downsampled iterative learning control. (English) Zbl 1222.93179
Summary: Cyclic pseudo-downsampled Iterative Learning Control (ILC) has shown advantages to achieve good learning performance for trajectories containing high-frequency components and has been verified on industrial robot application. This scheme is a multirate ILC in nature and downsamples the fast rate signals (with a sampling period \(T\)) to slow rate signals (with a sampling period \(mT\)) with a ratio \(m\). Then ILC is carried out on the downsampled signals and interpolates its output to a fast rate signal. For the next iteration, ILC scheme downsamples the signals with the same ratio \(m\) but at different sampling points with a time shift \(T\). This process is repeated on the iteration axis so that ILC updates the input of all the sampling points once every \(m\) cycles. By experiments [B. Zhang, D. Wang, Y. Ye, K. Zhou and Y. Wang, ‘Cyclic pseudo-downsampled iterative learning control for high performance tracking’, Control Engineering Practice 17, 957–965 (2009)], this scheme has been shown effective and comparisons with other relevant schemes demonstrate its superior performance. In this article, this cyclic pseudo-downsampled ILC scheme is examined analytically and proved mathematically to be stable and robust. Extensions and insights are also established based on the theoretical developments and simulation verification. pseudo-downsampled ILC scheme.

93D09 Robust stability
93C55 Discrete-time control/observation systems
68T05 Learning and adaptive systems in artificial intelligence
93C85 Automated systems (robots, etc.) in control theory
PDF BibTeX Cite
Full Text: DOI
[1] DOI: 10.1016/j.automatica.2006.11.020 · Zbl 1117.93075
[2] Chang C-K, Advances in Astronautical Science 76 pp 2035– (1992)
[3] Chen Y-Q, IEEE Symposium on Computational Intelligences in Robotics and Automation pp 396– (2001)
[4] DOI: 10.1080/002071700405860 · Zbl 1006.93597
[5] DOI: 10.1016/S0005-1098(02)00014-6 · Zbl 1013.93022
[6] DOI: 10.1016/S0005-1098(97)00068-X · Zbl 0881.93039
[7] DOI: 10.1080/002071700405905 · Zbl 1006.93598
[8] Moore KL, IEEE Symposium on Intelligences Control pp 45– (2001)
[9] DOI: 10.1016/j.automatica.2005.01.019 · Zbl 1086.93066
[10] Porter JD, International Journal of Adaptive Control and Signal Processing 19 pp 769– (2005) · Zbl 1127.93365
[11] DOI: 10.1016/S0005-1098(02)00003-1 · Zbl 1002.93508
[12] DOI: 10.1016/S0005-1098(98)00098-3 · Zbl 0961.93029
[13] Wang D, International Journal of Control 77 pp 1189– (2005) · Zbl 1070.93024
[14] DOI: 10.1109/TMECH.2005.848297
[15] DOI: 10.1109/TSMCB.2004.841411
[16] Zhang B, Proceedings of the American Control Conference pp 244– (2006)
[17] DOI: 10.1080/00207170600982153 · Zbl 1117.93045
[18] DOI: 10.1002/rnc.1232 · Zbl 1284.93153
[19] DOI: 10.1016/j.conengprac.2009.02.016
[20] Zheng D-N, Proceedings of the American Control Conference pp 4512– (2003)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.