In this paper, iterative learning control (ILC) is considered to solve the tracking problem of time-varying linear stochastic systems with randomly varying trial lengths. Using the two-dimensional Kalman filtering technique, the authors can establish a recursive framework for designing the learning gain matrix along both time and iteration axes by optimizing the trace of input error covariance matrix. It is strictly proved that the input error converges to zero asymptotically in mean square sense and thus the tracking error covariance converges. The extensions to that prior distribution of nonuniform trial lengths is unknown are also investigated with an asymptotical estimation method. Numerical simulations are provided to verify the effectiveness of the proposed framework.

中文翻译：

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随机变化试用长度的迭代学习控制的二维方法

在本文中，考虑迭代学习控制（ILC）来解决具有随机变化的试验长度的时变线性随机系统的跟踪问题。使用二维卡尔曼滤波技术，作者可以通过优化输入误差协方差矩阵的迹线，建立一个沿时间和迭代轴设计学习增益矩阵的递归框架。严格证明，输入误差在均方意义上渐近收敛到零，因此跟踪误差协方差收敛。还使用渐近估计方法研究了未知试验长度之前分布的扩展情况。提供数值模拟以验证所提出框架的有效性。