For data-driven iterative learning control (ILC) methods, both the model estimation and controller design problems are converted to parameter estimation problems for some chosen model structures. It is well-known that if the model order is not chosen carefully, models with either large variance or large bias would be resulted, which is one of the obstacles to further improve the modeling and tracking performances of data-driven ILC in practice. An emerging trend in the system identification community to deal with this issue is using regularization instead of the statistical tests, e.g., AIC, BIC, and one of the representatives is the so-called kernel-based regularization method (KRM). In this paper, we integrate KRM into data-driven ILC to handle a class of repetitive linear time-varying systems, and moreover, we show that the proposed method has ultimately bounded tracking error in the iteration domain. The numerical simulation results show that in contrast with the least squares method and some existing data-driven ILC methods, the proposed one can give faster convergence speed, better accuracy and robustness in terms of the tracking performance.

对于数据驱动的迭代学习控制 (ILC) 方法，模型估计和控制器设计问题都转换为某些所选模型结构的参数估计问题。众所周知，如果不仔细选择模型阶数，将会产生方差大或偏差大的模型，这是在实践中进一步提高数据驱动 ILC 建模和跟踪性能的障碍之一。系统识别界处理这个问题的一个新兴趋势是使用正则化来代替统计检验，例如AIC、BIC，其中代表之一就是所谓的基于内核的正则化方法（KRM）。在本文中，我们将 KRM 集成到数据驱动的 ILC 中来处理一类重复的线性时变系统，而且，我们表明，所提出的方法最终在迭代域中限制了跟踪误差。数值仿真结果表明，与最小二乘法和一些现有的数据驱动ILC方法相比，所提出的方法在跟踪性能方面具有更快的收敛速度、更好的精度和鲁棒性。