This article studies the conflicting goals of high-precision tracking and quick convergence speed, which is a longstanding problem in the learning control of stochastic systems. In such systems, a decreasing gain sequence is necessary to ensure the asymptotic convergence of the generated input sequence to a fixed limit. However, the convergence speed is adversely affected by gain sequences of this nature. In this article, we propose a novel multistage learning control strategy to resolve this conflict, where each stage consists of several iterations. The learning gain remains constant in each stage but is reduced at the transition from a given stage to the subsequent stage. The switching iteration between two stages is determined by the tracking performance index of the contracted input error and the accumulated noise drift. Furthermore, an improved mechanism is proposed to optimize the lengths of the different stages. The asymptotic convergence of the input sequence generated by the newly proposed strategy is strictly established by thoroughly analyzing the properties of the proposed gain sequence. Numerical simulations are presented to verify the theoretical results.

中文翻译：

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随机学习控制的新型自适应增益策略

本文研究了高精度跟踪和快速收敛速度的冲突目标，这是随机系统学习控制中长期存在的问题。在此类系统中，需要减小增益序列以确保生成的输入序列渐近收敛到固定极限。然而，收敛速度受到这种性质的增益序列的不利影响。在本文中，我们提出了一种新颖的多阶段学习控制策略来解决这种冲突，其中每个阶段都包含多次迭代。每个阶段的学习增益保持不变，但在从给定阶段到后续阶段的过渡时会减少。两个阶段之间的切换迭代由收缩输入误差和累积噪声漂移的跟踪性能指标决定。此外，还提出了一种改进的机制来优化不同阶段的长度。通过彻底分析所提出的增益序列的性质，严格建立了新提出的策略生成的输入序列的渐近收敛性。提出了数值模拟来验证理论结果。