Koopman-Theoretic Modeling of Quasiperiodically Driven Systems: Example of Signalized Traffic Corridor
提出一种数据驱动框架，利用再生核希尔伯特空间和遍历理论重建准周期驱动系统，并以九个连续信号化交通路口的数据为例，准确重构排队长度并实现稳定长期预测。
This article presents a novel approach to analyzing quasiperiodically driven dynamical systems. It presents a holistic data-driven framework for reconstructing such a system and gaining insights into its dynamical behavior. A quasiperiodically driven dynamics has two components: 1) the quasiperiodic driving source with generating frequencies and 2) the driven nonlinear dynamics. The driving dynamics are reconstructed by accurately computing a large number of Koopman eigenfrequencies, using techniques based on the theory of reproducing kernel Hilbert space (RKHS) and from ergodic theory. Unlike Fourier analysis and dynamic mode decomposition (DMD), the proposed framework can analyze systems/signals with nondominant or absent periodic components. The driven system is next reconstructed by continuing to use the RKHS framework. As a case study, we investigate data collected from a corridor of nine consecutive signalized traffic intersections. The proposed framework provides insights into generating frequencies and associated modes, accurately reconstructs the queue lengths at the signalized intersections, and makes stable long-term forecasts. The unique contributions of this article are spread across multiple domains. It includes the novel modeling framework for quasiperiodically driven systems, a computationally efficient approach able to handle a large amount of data, utilization of true Koopman eigenfrequencies, and an illustration of the proposed approach on a corridor of signalized traffic intersections.