CAREER: Control Design for Dynamical Network Flows with Applications to Transportation

随着我们的社会越来越依赖于交通、通信、水、电和天然气等关键基础设施网络，它们的高效和弹性运营变得越来越重要。因此，美国国家工程院确定的工程重大挑战之一是恢复和改善城市基础设施系统。然而，正如美国土木工程师协会最近的评估所显示的那样，我们的基础设施系统的状况仍然不符合标准，如果没有大规模的投资，情况可能会继续如此。由于预计需求将大幅增长，维持现状的未来基础设施系统即使在目前往往不足的水平上也无法发挥作用。人们越来越意识到，利用传感、驱动和信息技术可以大幅提高这些系统的性能。这些网络技术有可能赋予我们的基础设施网络在中断情况下动态响应需求，供应甚至物理属性变化的能力。然而，现有的控制基础设施网络的方法不足以实现这种能力的潜力。这是因为它们要么是启发式的，没有正式的性能保证;或者它们采用静态抽象，因此只适用于长期规划;或者动态框架仅用于模拟和分析目的，很少或根本不考虑控制设计。该项目将开发一个关于智能基础设施网络严格控制设计的综合研究和教育计划，特别强调交通。与当地交通和规划机构的合作将促进从研究到实践的快速过渡。推广活动包括开发一个互动交通模拟器，该模拟器还将作为模拟动态驾驶员行为的实验测试台;以及互动网络阻断游戏，向公众演示级联故障和网络鲁棒性的概念。教育活动包括编制关于分析、控制和估计基础设施网络的新课程。研究机会将扩大为本科生实现控制算法的专业交通软件生成案例研究，这将用于我们与交通机构的互动。南加州大学的现有项目将被用于将包容性教学实践融入教育活动，以解决女性、代表性不足和少数民族学生的保留问题。当前网络流理论研究主要包括快速计算网络最大流容量或最优流分配的算法，以及在固定路由策略下具有级联效应的动态网络流的数值分析。所提出的研究的智力价值是：（i）一个动态网络流框架，该框架模拟了网络拓扑中流的动态和跳跃之间的耦合，例如，由于级联故障，以及方便控制设计;（ii）在分析非线性动态系统的微分分析和收缩原则，并将其应用于分析和控制综合下提出的动态网络流的新进展;（iii）的计算框架，量化利润率的弹性方面的干扰产生过程，网络拓扑结构，和级联动态;（iv）通过动态信号控制将拟议工具应用于交通运输，并在网络设计中纳入弹性指标。弹性计算的余量将确定规范的网络流概念，除了经典的概念削减，从效率和弹性的角度来看，控制和动态的考虑下，作为网络性能的关键指标。除了直接强调动态网络流之外，该项目旨在为网络动态系统开发鲁棒控制理论的要素。

As our society is becoming more dependent on critical infrastructure networks such as transportation, communication, water, power, and gas, their efficient and resilient operation is becoming ever more important. Hence, one of the engineering grand challenges identified by the National Academy of Engineering is to restore and improve urban infrastructure systems. However, as recent evaluations by the American Society of Civil Engineers show, the state of our infrastructure systems continues to be substandard, and will likely remain so without massive investments. With significant growth in demand projected, a future infrastructure system that maintains the status quo will not function even at today's current, often inadequate, levels. It is increasingly being realized that leveraging sensing, actuation, and information technologies can achieve substantial improvements in the performance of these systems. These cyber technologies have the potential to endow our infrastructure networks with the capability to dynamically respond to changes in demand, supply, and even physical properties under disruptions. The existing approaches to control of infrastructure networks, however, are inadequate to realize the potential of this capability. This is because they are either heuristic with no formal performance guarantees; or they adopt static abstractions, and hence are useful only for long term planning; or the dynamical frameworks are used only for simulation and analysis purposes with little or no consideration for control design. The project will develop an integrated research and education program on rigorous control design for intelligent infrastructure networks, with a special emphasis on transportation. Collaborations with local transportation and planning agencies will facilitate rapid transition from research to practice. The outreach activities include development of an interactive traffic simulator, which would also serve as an experiment test bed to model dynamic driver behavior; and interactive network interdiction games to demonstrate the concepts of cascading failures and network robustness to general public. The education activities include development of new courses on analysis, control and estimation of infrastructure networks. Research opportunities will be expanded for undergraduates to implement control algorithms on professional transportation software to generate case studies, which will be used for our interactions with transportation agencies. Existing programs at the University of Southern California will be utilized to integrate inclusive teaching practices into educational activities in order to address retention of women, underrepresented and minority students.Network flow is a natural modeling paradigm for several infrastructure networks. The current state-of-the-art in theoretical network flow research primarily consists of algorithms for fast computation of maximum network flow capacity, or optimal flow distribution with respect to some performance metrics; and numerical analysis of dynamical network flows with cascade effects under fixed routing policies. The intellectual merits of the proposed research are: (i) a dynamical network flow framework that models coupling between dynamics of flow and jumps in network topology, e.g., due to cascading failures, as well as facilitates control design; (ii) new advancements in analysis for nonlinear dynamical systems using differential analysis and contraction principles, and applying them for analysis and control synthesis under proposed dynamical network flow; (iii) a computational framework for quantifying margins of resilience in terms of the disturbance generation process, network topology, and cascade dynamics; (iv) application of proposed tools to transportation through dynamic signal control, and inclusion of resilience metric in network design. The margin of resilience computations will identify canonical network flow concepts, besides the classical notion of cuts, as key indicators of network performance from efficiency and resilience perspective, under control and dynamical considerations. Beyond its immediate emphasis on dynamical network flows, the project aims to develop elements of robust control theory for networked dynamical systems.