Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering purposes. The introduction of a recent computationally efficient method in the context of fluid dynamics, which is based on the system dynamics decomposition to a set of normal modes in descending order, has overcome this long-lasting computational obstacle. The purely data-driven nature of Koopman operators holds the promise of capturing unknown and complex dynamics for reduced-order model generation and system identification, through which the rich machinery of linear control techniques can be utilized. Given the ongoing development of this research area and the many existing open problems in the fields of smart mobility and vehicle engineering, a survey of techniques and open challenges of applying Koopman operator theory to this vibrant area is warranted. This review focuses on the various solutions of the Koopman operator which have emerged in recent years, particularly those focusing on mobility applications, ranging from characterization and component-level control operations to vehicle performance and fleet management. Moreover, this comprehensive review of over 100 research papers highlights the breadth of ways Koopman operator theory has been applied to various vehicular applications with a detailed categorization of the applied Koopman operator-based algorithm type. Furthermore, this review paper discusses theoretical aspects of Koopman operator theory that have been largely neglected by the smart mobility and vehicle engineering community and yet have large potential for contributing to solving open problems in these areas.

翻译：库普曼算子理论已被证明是一种有前途的非线性系统辨识与全局线性化方法。近一个世纪以来，工程应用领域一直缺乏高效计算库普曼算子的手段。近期在流体动力学领域提出的基于系统动力学按降序分解为系列简正模态的高效计算方法，克服了这一长期存在的计算障碍。库普曼算子纯数据驱动的特性，使其有望通过降阶模型生成和系统辨识捕捉未知复杂动力学，进而运用丰富的线性控制技术体系。鉴于该研究领域的持续发展以及智能出行与车辆工程领域存在的诸多开放性问题，有必要对库普曼算子理论应用于这一活跃领域的技术方法与开放挑战进行综述。本综述聚焦近年来涌现的库普曼算子求解方案，特别关注面向出行应用的研究成果，涵盖从特性表征、部件级控制操作到整车性能与车队管理等多个层面。通过对100余篇研究论文的全面梳理，本文以库普曼算子算法类型为分类依据，系统展示了该理论在各类车辆应用中的广度。此外，本综述还讨论了智能出行与车辆工程界长期忽视但具有解决该领域开放性问题巨大潜力的库普曼算子理论层面问题。