This paper proposes an iterative learning control (ILC) algorithm with gain adaptation for discrete-time stochastic systems. The algorithm is based on Kesten's accelerated stochastic approximation (SA) algorithm. The gain adaptation uses only tracking error information, and, hence, is a data-driven adaptation approach. If stochastic noises account for a small proportion of the tracking error, the learning gain matrix remains constant with a high probability. If stochastic noises dominate the tracking error, the learning gain matrix is decreasing. Therefore, the new ILC algorithm converges more quickly than existing SA-based algorithms. In addition, the classic P-type ILC law for noise-free systems is a special case of the new ILC algorithm. The behaviors of the proposed ILC algorithm are demonstrated through examples.

中文翻译：

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随机系统增益自适应迭代学习控制算法

本文提出了一种用于离散时间随机系统的具有增益自适应的迭代学习控制 (ILC) 算法。该算法基于 Kesten 的加速随机逼近 (SA) 算法。增益自适应仅使用跟踪误差信息，因此是一种数据驱动的自适应方法。如果随机噪声占跟踪误差的一小部分，则学习增益矩阵很可能保持不变。如果随机噪声在跟踪误差中占主导地位，则学习增益矩阵会减小。因此，新的 ILC 算法比现有的基于 SA 的算法收敛得更快。此外，用于无噪声系统的经典 P 型 ILC 定律是新 ILC 算法的特例。通过示例演示了所提出的 ILC 算法的行为。