Stability and robustness analysis of cyclic pseudo-downsampled iterative learning control.

*(English)*Zbl 1222.93179Summary: 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.

##### MSC:

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 |

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\textit{B. Zhang} et al., Int. J. Control 83, No. 3, 651--659 (2010; Zbl 1222.93179)

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