The existing frequency-domain-based iterative learning control (ILC) methods are highly dependent on the mathematical models of the controlled systems. For linear discrete-time single-input single-output (SISO) systems with unknown mathematical models, this paper tries to present fully data-driven ILC designs in frequency domain. With the help of support vector machine (SVM), the input-output data of the linear discrete-time SISO system at the first repetition is utilised to constitute an adaptive Fourier decomposition (AFD) model. Then, based on the AFD model, a P-type ILC law and an extended D-type ILC law with data-driven determining techniques for learning gains are presented. It is noted that comparing with the conventional D-type ILC law, the newly proposed extended D-type ILC law exhibits superior tracking characteristic due to involving the frequency information during the ILC process. A numerical example is utilised to illustrate the effectiveness of the proposed ILC algorithms with the data-driven determining techniques for learning gains.

中文翻译：

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基于 AFD 的线性离散时间系统的频域 ILC 设计

现有的基于频域的迭代学习控制 (ILC) 方法高度依赖于受控系统的数学模型。对于具有未知数学模型的线性离散时间单输入单输出 (SISO) 系统，本文尝试在频域中呈现完全数据驱动的 ILC 设计。借助支持向量机(SVM)，利用线性离散时间SISO系统在第一次重复时的输入输出数据，构成自适应傅里叶分解(AFD)模型。然后，基于 AFD 模型，提出了 P 型 ILC 定律和扩展的 D 型 ILC 定律，它们具有数据驱动的学习增益确定技术。值得注意的是，与传统的 D 型 ILC 法相比，由于在 ILC 过程中涉及频率信息，新提出的扩展 D 型 ILC 定律表现出优异的跟踪特性。一个数值例子被用来说明所提出的 ILC 算法与数据驱动的学习增益确定技术的有效性。