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.

翻译：Koopman算子作为动力控制系统机器学习的理论基础，通过扩展动态模态分解（EDMD）对该算子进行启发式逼近。本文提出稳定性与认证导向的EDMD（SafEDMD）：一种新型基于EDMD的学习架构，该架构兼具严格认证机制，能够以数据驱动方式生成可靠的替代模型。为确保SafEDMD的可靠性，我们推导了比例误差界，该误差界在原点处消失且专为控制任务设计，进而实现基于半定规划的认证控制器设计。通过多个基准算例阐释所开发方法，并突出相较于现有技术的优势。