用强化学习思路选最优控制器，能实时发现不稳定的控制方案。
Online Learning for Supervisory Switching Control
- 将多臂赌博机算法引入控制领域，动态评估多个控制器性能。
- 在 $O(N \log^2 N)$ 步内找到匹配的控制器，且对扰动有有限增益。
- 无需假设系统稳定，适合测试可能不稳定的控制器。
我们研究部分可观测线性动态系统的监督切换控制问题，目标是通过周期性地从 $N$ 个候选控制器中选择，识别并部署适用于未知系统的控制器，其中部分控制器可能使系统失稳。经典基于估计器的监督控制虽保证渐近稳定性，但缺乏定量的有限时间性能界。而当前在线学习与系统辨识中的非渐近方法需强假设（如系统稳定性），这在控制场景下不适用，无法测试潜在不稳定的控制器。为此，我们提出一种新颖的非渐近分析框架，将多臂赌博机算法适配至控制理论场景。所提数据驱动算法通过利用系统可观测性设计评分准则，分离状态历史影响，从而实现对不稳定控制器的检测与精确系统辨识。我们提出两种算法变体，均具备无维度的有限时间保证：每个算法可在 $O(N \log^2 N)$ 步内识别出匹配控制器，同时对系统扰动保持有限 $L_2$-增益。
原文摘要 · Abstract (English)
We study supervisory switching control for partially-observed linear dynamical systems. The objective is to identify and deploy a suitable controller for the unknown system by periodically selecting among a collection of $N$ candidate controllers, some of which may destabilize the underlying system. While classical estimator-based supervisory control guarantees asymptotic stability, it lacks quantitative finite-time performance bounds. Conversely, current non-asymptotic methods in both online learning and system identification require restrictive assumptions that are incompatible in a control setting, such as system stability, which preclude testing potentially unstable controllers. To bridge this gap, we propose a novel, non-asymptotic analysis of supervisory control that adapts multi-armed bandit algorithms to a control-theoretic setting. The proposed data-driven algorithm evaluates candidate controllers via scoring criteria that leverage system observability to isolate the effects of state history, enabling both detection of destabilizing controllers and accurate system identification. We present two algorithmic variants with dimension-free, finite-time guarantees, where each identifies the matching controller in $O(N \log^2 N)$ steps, while simultaneously achieving finite $L_2$-gain with respect to system disturbances.
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