Kernel-based Regularized Iterative Learning Control of Repetitive Linear Time-varying Systems⁎Yu's and Chen's contribution to this work was supported by the Thousand Youth Talents Plan funded by the central government of China, the general project funded by NSFC under contract No. 61773329, the Shenzhen research projects funded by the Shenzhen Science and Technology Innovation Council under contract No. Ji-20170189, the President's grant under contract No. PF. 01.000249 and the Start-up grant under contract No. 2014.0003.23 funded by CUHKSZ. Mu's contribution to this work was supported (in part) by the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No. XDA27000000. Ljung's contribution to this work was supported by the Swedish Research Council, contract 2019-04956 and by Vinnova's center LINKSIC. Issue 7 (2021) - Yu, Xian; Chen, Tianshi; Mu, Biqiang; Ljung, Lennart
Abstract: The selections for the model orders and the number of controller parameters have not been discussed for many data-driven iterative learning control (ILC) methods. If they are not chosen carefully, the estimated model and designed controller will lead to either large variance or large bias. In this paper we try to use the kernel-based regularization method (KRM) to handle the model estimation problem and the controller design problem for unknown repetitive linear time-varying systems. In particular, we have used the diagonal correlated kernel and the marginal likelihood maximization method for the two problems. Numerical simulation results show that smaller mean square errors for each time instant are obtained by using the proposed ILC method in comparison with an existing data-driven ILC approach.