The nonuniform trial length problem, which causes information dropout in learning, is very common in various control systems such as robotics and motion control systems. This paper presents a comprehensive survey of recent progress on iterative learning control with randomly varying trial lengths. Related works are reviewed in three dimensions: model, synthesis, and convergence analysis. Specifically, we first present both random and deterministic models of varying trial lengths to provide a mathematical description and to reveal the effects and difficulties of nonuniform trial lengths. Then, control synthesis focusing on compensation mechanisms for the missing information and key ideas in designing control algorithms are summarized. Lastly, four representative convergence analysis approaches are elaborated, including deterministic analysis approach, switching system approach, contraction mapping approach, and composite energy function approach. Promising research directions and open issues in this area are also discussed.

在学习过程中导致信息丢失的不均匀试验长度问题在各种控制系统（例如机器人和运动控制系统）中非常普遍。本文对随机学习长度不同的迭代学习控制的最新进展进行了全面的综述。相关作品从三个方面进行了回顾：模型，综合和收敛性分析。具体而言，我们首先介绍了不同试验长度的随机模型和确定性模型，以提供数学描述并揭示不均匀试验长度的影响和困难。然后，总结了针对丢失信息的补偿机制的控制综合以及设计控制算法的关键思想。最后，阐述了四种代表性的收敛分析方法，包括确定性分析方法，交换系统方法，收缩映射方法和复合能量函数方法。还讨论了该领域有希望的研究方向和未解决的问题。