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From Noisy Data to Feedback Controllers: Nonconservative Design via a Matrix S-Lemma
IEEE Transactions on Automatic Control ( IF 6.8 ) Pub Date : 2020-12-25 , DOI: 10.1109/tac.2020.3047577
Henk J. van Waarde , M. Kanat Camlibel , Mehran Mesbahi

In this article, we propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient of our design is a new matrix S-lemma that will be proven in this article. We provide both strict and nonstrict versions of this S-lemma, which are of interest in their own right. Thereafter, we will apply these results to data-driven control. In particular, we will derive nonconservative design methods for quadratic stabilization, $\mathcal {H}_2$ and $\mathcal {H}_{\infty }$ control, all in terms of data-based linear matrix inequalities. In contrast to previous work, the dimensions of our decision variables are independent of the time horizon of the experiment. Our approach, thus, enables control design from large datasets.

中文翻译:

从噪声数据到反馈控制器:通过矩阵 S 引理的非保守设计

在本文中,我们提出了一种新方法,可以直接从嘈杂的输入/状态数据中获取未知动态系统的反馈控制器。我们设计的关键要素是一个新的矩阵 S 引理,本文将对其进行证明。我们提供了这个 S 引理的严格和非严格版本,它们本身就很有趣。此后,我们将把这些结果应用于数据驱动控制。特别是,我们将推导出二次稳定的非保守设计方法,$\mathcal {H}_2$$\mathcal {H}_{\infty }$控制,都是基于数据的线性矩阵不等式。与之前的工作相比,我们的决策变量的维度与实验的时间范围无关。因此,我们的方法可以从大型数据集进行控制设计。
更新日期:2020-12-25
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