A Behavioral Approach to Data-Driven Control With Noisy Input-Output Data

• 成果类型: Article
• 署名作者: van Waarde, Henk J.; Eising, Jaap; Camlibel, M. Kanat; Trentelman, Harry L.
• 署名单位: University of Groningen; University of California System; University of California San Diego
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3275014
• 发表日期: 2024
• 页码: 813-827
• 关键词: Linear matrix inequalities; Noise measurement; Behavioral sciences; mathematical models; Adaptive control; Lyapunov methods; asymptotic stability; Behavioral approach; Data-driven control; quadratic matrix inequalities (QMIs); Robust control; S-procedure

摘要

This article deals with data-driven stability analysis and feedback stabilization of linear input-output systems in autoregressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some unknown AR system. Data-based tests are then developed to analyze whether the unknown system is stable, or to verify whether a stabilizing dynamic feedback controller exists. If so, stabilizing controllers are computed using the data. In order to do this, we employ the behavioral approach to systems and control, meaning a departure from existing methods in data driven control. Our results heavily rely on a characterization of asymptotic stability of systems in AR form using the notion of quadratic difference form as a natural framework for Lyapunov functions of autonomous AR systems. We introduce the concepts of informative data for quadratic stability and quadratic stabilization in the context of input-output AR systems and establish necessary and sufficient conditions for these properties to hold. In addition, this article will build on results on quadratic matrix inequalities and a matrix version of Yakubovich's S-lemma.