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

在几个大型复杂系统中，如交通网络、电网和金融市场，都观察到了全球新兴模式。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，这些新出现的模式通常决定了拥堵动态，并准备随着可以相互通信的联网车辆的引入而经历一场变革性的变化。因此，我们观察这些模式的能力在有效管理向更智能的交通网络的过渡以及改善系统性能和减少拥堵成本方面发挥着关键作用。这项研究试图回答有关观察这些模式的合适规模的问题。此外，这项工作还试图评估不同的联网车辆渗透率对观察交通紧急模式的能力的影响。这项工作对于显著提高我们监测、预测和控制突发拥堵事件的能力具有很大的潜力。就交通流应用而言，这项研究可能有助于降低全球每年估计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，并使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，创建视觉吸引力和清晰的图形材料，以吸引本科生和研究生以及普通公众。该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的紧急现象所需的空间尺度和模型阶数。在较窄的交通流背景下，该项目试图建立多车道高速公路上观察突发拥堵事件的建模要求，并以比现有预测模型更高的精度预测此类行为。该方法将通过明确地将空间尺度纳入过程来修改现有的基于Krylov子空间的模型降阶技术。更重要的是，这项工作的新贡献将是借用统计力学领域的重整化群理论的控制论表述，以了解涌现动力学的可观性如何依赖于空间尺度。这项研究将包括在控制论的背景下研究复杂系统的可观性的空间相关性。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.