From Noisy Data to Feedback Controllers: Nonconservative Design via a Matrix S-Lemma

• 成果类型: Article
• 署名作者: van Waarde, Henk J.; Camlibel, M. Kanat; Mesbahi, Mehran
• 署名单位: University of Groningen; University of Groningen; University of Washington; University of Washington Seattle
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3047577
• 发表日期: 2022
• 页码: 162-175
• 关键词: data-driven control; LMIs; Robust control; uncertain systems

摘要

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, H-2 and H-infinity 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.