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：Koopman算子理论已被证明是非线性系统辨识与全局线性化的有效方法。近一个世纪以来，工程应用领域始终缺乏高效计算Koopman算子的手段。近年来，流体动力学领域引入了一种基于系统动力学按降序分解为正则模态的计算高效方法，突破了这一长期存在的计算瓶颈。Koopman算子纯数据驱动的特性，有望通过降阶模型生成和系统辨识捕获未知复杂动力学，进而利用线性控制理论的丰富工具。鉴于该研究领域持续发展以及智能出行与车辆工程领域尚存的诸多开放性难题，有必要对Koopman算子理论在此活跃领域的应用技术与挑战进行综述。本综述聚焦近年来涌现的各类Koopman算子求解方案，尤其关注出行应用——涵盖从系统表征与部件级控制操作到车辆性能及车队管理。通过对100余篇研究论文的全面回顾，本文以应用Koopman算子算法类型为详细分类依据，系统阐述了该理论在各类车辆应用中的广泛应用场景。此外，本文还讨论了智能出行与车辆工程界长期忽视、却对解决该领域开放性问题具有巨大潜力的Koopman算子理论若干理论层面。