AI 中文总结
本文针对切换线性系统稳定性分析，提出带有限样本保证的间接数据驱动控制框架，扩展直接方法以处理测量噪声，实验表明中高噪声下间接方法鲁棒性更优。
AI 中文摘要
数据驱动控制中的一个核心方法论问题是采用直接方法还是间接方法。直接方法直接从数据中推断控制器或证书，而间接方法则先辨识系统模型，再应用基于模型的控制技术。近年来，直接方法的发展已为不同场景下切换线性系统的数据驱动稳定性分析提供了有限样本保证，但对于间接方法，此类保证仍难以获得。本文中，我们采用间接方法与二次李雅普诺夫分析，提出了一种基于噪声状态测量的切换线性系统稳定性分析新框架，该框架对系统收敛速率具有有限样本保证。为实现这一目标，我们将机器学习的泛化界、系统辨识与二次李雅普诺夫分析的敏感性分析相结合。为便于对比，我们还扩展了现有的直接数据驱动方法，使其能够处理文献中当前仅有的有界噪声情况之外的测量噪声。最后，我们通过数值实验对比了两种方法，结果表明，在中高噪声水平下，间接方法比直接方法能提供更严格的概率保证，且对噪声和异常值具有更强的鲁棒性。
英文摘要
A central methodological question in data-driven control is whether to adopt a direct or indirect approach. Direct methods infer a controller or certificate directly from data, while indirect methods first identify a system model and then apply model-based control techniques. Recent developments of the direct method have led to finite-sample guarantees for the data-driven stability analysis of switched linear systems under various settings. However, for the indirect method, such guarantees remain largely elusive. In this paper, we provide a novel framework for the stability analysis of switched linear systems from noisy state measurements, using the indirect approach and quadratic Lyapunov analysis. Our framework comes with finite-sample guarantees on the convergence rate of the system. For that, we combine generalization bounds from machine learning and system identification with sensitivity analysis from quadratic Lyapunov analysis. To enable comparison, we also extend existing direct data-driven methods to handle measurement noise beyond the bounded noise case currently available in the literature. Finally, we compare the two approaches through numerical experiments, revealing that under moderate-to-high noise levels the indirect approach yields tighter probabilistic guarantees as well as greater robustness to noise and outliers than the direct approach
CommentsPreprint version. Submitted to Automatica. (Fixed version - the previous preprint on arXiv was not the finished one submitted to Automatica.)
