The Koopman operator serves as the theoretical backbone for machine learning of dynamical control systems, where the operator is heuristically approximated by extended dynamic mode decomposition (EDMD). In this paper, we propose Stability- and certificate-oriented EDMD (SafEDMD): a novel EDMD-based learning architecture which comes along with rigorous certificates, resulting in a reliable surrogate model generated in a data-driven fashion. To ensure the trustworthiness of SafEDMD, we derive proportional error bounds, which vanish at the origin and are tailored to control tasks, leading to certified controller design based on semi-definite programming. We illustrate the developed method by means of several benchmark examples and highlight the advantages over state-of-the-art methods.

翻译：Koopman算符作为动力控制系统机器学习的理论基础，其通过扩展动态模态分解（EDMD）进行启发式近似。本文提出面向稳定性与证书的EDMD（SafEDMD）：一种基于EDMD的新型学习架构，该架构具有严格的认证机制，能够以数据驱动方式生成可靠的代理模型。为确保SafEDMD的可信性，我们推导出随原点消失且面向控制任务的成比例误差界，进而实现基于半定规划的认证控制器设计。通过多个基准算例验证所提方法，并突出其相较现有技术方法的优势。