A Koopman-backstepping approach to data-driven robust output regulation for linear parabolic systems

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2025-08-22 DOI:10.1016/j.automatica.2025.112538

Joachim Deutscher, Julian Zimmer

引用次数: 0

Abstract

In this paper a solution of the data-driven robust output regulation problem for linear parabolic systems is presented. Both the system as well as the ODE, i.e., the disturbance model, describing the disturbances are unknown, but finite-time sequential data obtained from measurements of the output to be controlled and additional boundary outputs are available. The data-driven controller is designed in the Koopman operator framework for PDEs, where the Koopman modes and eigenvalues are obtained from data using Hankel-DMD. It is shown that all system parameters and the eigenvalues of the disturbance model can be recovered from the available measurements by solving an inverse Sturm–Liouville problem. This allows to directly apply backstepping methods for the robust regulator design. For this, closed-loop stability in the presence of small errors in the Hankel-DMD is verified in the nominal case. Robust output regulation is shown for non-destabilizing model uncertainties. A numerical example demonstrates the results of the paper.

查看原文本刊更多论文

线性抛物型系统数据驱动鲁棒输出调节的Koopman-backstepping方法

本文给出了线性抛物型系统数据驱动鲁棒输出调节问题的一个解。系统和ODE（即描述扰动的扰动模型）都是未知的，但是从要控制的输出和附加边界输出的测量中获得的有限时间序列数据是可用的。数据驱动控制器采用Koopman算子框架，利用Hankel-DMD从数据中获得库普曼模态和特征值。结果表明，通过求解逆Sturm-Liouville问题，可以从可用的测量数据中恢复系统的所有参数和扰动模型的特征值。这允许直接应用backstepping方法稳健调节器设计。为此，在名义情况下，验证了Hankel-DMD存在小误差时的闭环稳定性。对非不稳定模型的不确定性进行了鲁棒输出调节。数值算例验证了本文的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.