arXiv：cs.LG· Igor Mezi\'c, Jorge Cort\'es, Karl Worthmann, Mircea Lazar, Armin Lederer·· 3 小时前
Koopman 算子理论：基础、控制与应用
Koopman operator theory: fundamentals, control, and applications
AI 导读
这篇教程论文系统介绍了 Koopman 算子理论及其在系统与控制中的应用，该算子能通过可观测函数为高度复杂的非线性动力系统提供全局线性表示。
正文
Abstract:The Koopman operator has gained considerable attention due to its ability to provide a global linear representation of highly complex dynamical systems. The operator describes nonlinear dynamics in a linear way through the lens of real- or complex-valued observable functions. Data-driven techniques, like extended dynamic mode decomposition (EDMD), kernel EDMD, and machine-learning methods, can be used to generate finite-dimensional approximations accompanied by finite-data error bounds. In this tutorial paper, we provide a concise introduction into Koopman operator theory and its use in systems and control. A particular focus is put on data-driven surrogate models, their extension to systems with inputs, and controller design using Koopman operator theory. Moreover, we demonstrate the key techniques, i.e., EDMD and Koopman MPC. To this end, we provide simulation studies including source code on GitHub to enable the interested reader to experience the Koopman operator in systems and control step by step.
| Subjects: | Systems and Control (eess.SY); Machine Learning (cs.LG) |
| Cite as: | arXiv:2607.01819 [eess.SY] |
| (or arXiv:2607.01819v2 [eess.SY] for this version) | |
| https://doi.org/10.48550/arXiv.2607.01819 arXiv-issued DOI via DataCite |
Submission history
From: Armin Lederer [view email]
[v1]
Thu, 2 Jul 2026 07:31:47 UTC (761 KB)
[v2]
Thu, 8 Oct 2026 07:30:38 UTC (788 KB)
来源：arXiv：cs.LG · arxiv.org