Scale-Dependent Observability of Emergent Dynamics: Application to Traffic Flow with Connected Vehicles

在几个大型复杂系统中可以观察到全球涌现模式，例如交通网络、电网和金融市场。了解这些动态演变的行为模式对于解决与此类系统相关的问题非常重要。例如，在交通网络中，这些新兴模式通常决定了拥堵动态，并且随着可以相互通信的互联车辆的引入，这些模式将发生革命性的变化。因此，我们观察这种模式的能力在有效管理向智能交通网络的过渡以及提高系统性能和降低拥堵成本方面发挥着关键作用。这项研究试图回答有关这些模式可能被最好地观察到的适当尺度的问题。此外，本研究还试图评估联网车辆的不同渗透率对观察交通中紧急模式的能力的影响。这项工作具有极大的潜力，可以显著提高我们对紧急拥堵事件发生的监测、预测和控制能力。以交通流应用为例，这项研究可以帮助减少全球每年估计为数千亿美元的拥堵成本。在这项研究中开发的技术将增强我们关于如何观察紧急行为的基本知识，并利用这些知识来分析和解决与其他几个复杂系统相关的问题。该项目还具有高度创新的教育计划，创建视觉上吸引人的清晰图形材料，以吸引本科生和研究生以及公众。本研究项目的主要目标是创建一种严格的方法来确定观察和预测复杂系统中出现的现象所需的空间尺度和模型顺序。在较窄的交通流背景下，该项目旨在建立在多车道高速公路上观察紧急拥堵事件的建模要求，并以比当前预测模型更高的准确性预测此类行为。该方法将修改现有的基于Krylov子空间的模型降阶技术，明确地将空间尺度纳入到过程中。更重要的是，这项工作的新贡献将是从统计力学领域借鉴的重整化群论的控制理论公式，以获得对紧急动力学的可观测性如何依赖于空间尺度的理解。本研究将包括在控制理论背景下研究复杂系统中可观测性的空间依赖性。这项工作也将有助于研究渗透率（即传感器网络在复杂系统中的分布）如何影响复杂交通流动力学中紧急行为的可观察性。

Global emergent patterns are observed in several large-scale complex systems, such as transportation networks, power grids, and financial markets. Gaining understanding of these dynamically evolving behavioral patterns is very important to solve problems associated with such systems. For example, in transportation networks, these emergent patterns usually dictate congestion dynamics and are poised to undergo a transformative change with the introduction of connected vehicles that can communicate with each other. Consequently, our ability to observe such patterns plays a critical role in effectively managing the transition to a smarter transportation network as well as in improving system performance and reducing congestion costs. This research seeks to answer questions about the appropriate scale at which these patterns may be best observed. Additionally, this work also seeks to assess the effect of varying penetration rates of connected vehicles on the ability to observe emergent patterns in traffic. This work has a great potential to significantly improve our ability to monitor, predict and control the occurrence of emergent congestion events. In the case of traffic flow applications, this study could help reduce worldwide congestion costs that are estimated to be in several hundreds of billions of US dollars annually. The techniques developed during this study will enhance our fundamental knowledge about how to observe the emergent behavior and use this knowledge to analyze and solve the problems associated with several other complex systems. The project also has highly innovative educational plan of creating visually appealing and lucid graphics material to engage undergraduate and graduate students, as well as the general public.The primary objective of this research project is to create a rigorous methodology to determine the spatial scale and model order required to observe and predict emergent phenomena in complex systems. In a narrower context of traffic flow, the project seeks to establish the modeling requirements for observing emergent congestion events on a multi-lane highway, and predicting such behavior with better accuracy than current prediction models. The approach will modify existing Krylov subspace-based model order reduction techniques by explicitly incorporating spatial scales into the process. More importantly, the novel contribution of this work will be the control-theoretic formulation of the renormalization group theory borrowed from the field of statistical mechanics to gain an understanding of how the observability of emergent dynamics depends on spatial scale. The research will include the study of spatial dependence of observability in complex systems in a control-theoretic setting. This work will also contribute to the study of how penetration rate (i.e., the distribution of a sensor network in a complex system) impacts the observability of emergent behavior in complex traffic flow dynamics.