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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.

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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