How to establish control design methods for learning systems that are subjected to the stochastic uncertainties becomes a topic of practical importance in the control field. This paper deals with the stochastic iterative learning control (ILC) problems for linear time-varying systems subject to measurement noises and changing durations. The lengths of the changing durations are modeled as a Markov chain with finite states. By exploring the essential trackability problem, we develop a trackability-based design and analysis framework for the stochastic ILC systems. Besides, we design three trackability-based P-type stochastic ILC updating laws to achieve the tracking tasks, with some simple gain matrix selection conditions. Further, the convergence results for the stochastic ILC systems in both the almost-sure and mean-square senses are developed. Two illustrative examples are included to demonstrate the effectiveness of the trackability-based stochastic ILC results.

中文翻译：

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随机学习系统在变化的持续时间内的跟踪控制


如何建立具有随机不确定性的学习系统的控制设计方法成为控制领域具有实际意义的课题。本文研究了受测量噪声和持续时间变化影响的线性时变系统的随机迭代学习控制（ILC）问题。变化持续时间的长度被建模为具有有限状态的马尔可夫链。通过探索基本的可跟踪性问题，我们为随机 ILC 系统开发了一个基于可跟踪性的设计和分析框架。此外，我们设计了三种基于可跟踪性的P型随机ILC更新律来实现跟踪任务，并具有一些简单的增益矩阵选择条件。此外，还开发了随机 ILC 系统在几乎确定和均方意义上的收敛结果。其中包括两个说明性示例，以证明基于可跟踪性的随机 ILC 结果的有效性。