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 trustworthiness of SafEDMD, we derive proportional error bounds, which vanish at the origin and are tailored for control tasks, leading to certified controller design based on semi-definite programming. We illustrate the developed machinery by means of several benchmark examples and highlight the advantages over state-of-the-art methods.

本研究提出了基于稳定性和证书的扩展动态模态分解（SafEDMD）的学习架构，该架构通过严格的证书生成可靠的、数据驱动的代理模型，进一步得出了在控制任务中基于半定编程的认证控制器设计的误差界。通过多个基准示例展示了所开发机制的优势，并指出了与现有方法的区别。

SafEDMD：针对数据驱动的非线性动力系统控制的认证学习架构