Collaborative Research: Closed-loop Optimization and Control of Physical Networks Subject to Dynamic Costs, Constraints, and Disturbances

该项目将推进一个全新的控制框架，利用异构数据流来优化复杂和动态的网络系统的行为，这些系统具有普遍的传感和计算能力，可以在不确定和变化的环境中运行。现有的主力机控制和优化方法假定了很大的时间尺度分离，足以证明优化和控制任务完全解耦。然而，对于现代关键基础设施和社交平台来说，这种假设越来越不成立。该项目代表了一种新的方法，通过使用新的数学分析和综合原理来控制代理的集体行为和潜在的物理动力学，在与底层物理和物流系统的动力学相当的时间尺度上进行最佳和可靠的决策。关键概念是不断推动动力系统朝着优化问题的解决轨迹发展，这些问题具有随时间变化的成本、约束和输入。在未来交通网络的背景下，这种方法与高效、可持续地运送人员和货物的目标以及连接和自动驾驶车辆的集成非常一致。类似的应用机会出现在能源、机器人和自主系统等领域，具有通过多个异构物理和虚拟网络相互作用的相互连接的合作和非合作代理的共同特征。该项目还将通过一项全面的外展和教育计划影响本科生和研究生工程专业学生，以及K-12学生，其中包括STEM营地，参与活动，促进女学生和来自服务不足社区和少数民族学校的学生进入STEM管道，以及课程改进举措。网络系统和关键基础设施中的传统决策架构基于基于模型的网络级优化（以前馈方式产生设定值）和局部闭环控制（在拒绝干扰的同时调节动态系统到设定值）之间的明确时空界限。这些传统架构的操作方式在以下情况下运行良好：物理系统的底层动态比网络级优化任务所需的解决时间慢，网络模型和数据结构可用，并且可以及时可靠地广泛收集问题输入。然而，这样的假设在动态设置中变得越来越不充分，因为批量方法无法在与网络物理系统的动态相匹配的时间尺度上解决潜在的优化问题，物理模型（嵌入到优化任务中）难以准确估计，并且（未知的）干扰演变迅速且不可预测。该项目将生成新的数学原理，用于综合和分析基于在线数据的算法，这些算法将驱动代理的集体行为和物理动力学达到所需的操作点。特别是，期望的平衡点与时变优化问题的解轨迹相吻合，这些优化问题形式化了与动力系统相关的性能指标和操作约束。所研究的互联系统框架压缩了控制和优化任务之间的时间尺度，以持续驱动物理系统的动态行为达到网络最优和稳定点。该研究旨在扩展该项目愿景可以应用的问题类别，开发具有信息流的预测控制器，并为互联系统合成新颖的分布式算法解决方案。技术方法侧重于将网络交通系统作为实现理论和算法进步的舞台，并提供创新的控制和优化策略。除交通运输外，该技术还有望在更广泛的优化和控制领域得到推广，应用于流行病控制、机器人网络、社交网络和能源基础设施等多个领域。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will advance a fundamentally new control framework, utilizing streams of heterogeneous data to optimize the behavior of complex and dynamic networked systems with pervasive sensing and computing capabilities, operating in uncertain and changing environments. Existing workhorse control and optimization methodologies assume a large separation of time scales, sufficient to justify complete decoupling of the optimization and control tasks. However, this assumption is increasingly invalid for modern critical infrastructure and social platforms. This project represents a new approach for optimal and reliable decision-making on time scales comparable to the dynamics of the underlying physical and logistic systems, by using new mathematical principles of analysis and synthesis to control the collective behavior of agents and the underlying physical dynamics. The key concept is to continuously drive the dynamical system towards solution trajectories of optimization problems that have costs, constraints, and inputs which change over time. In the context of future transportation networks, the approach is well-aligned with the objective of moving people and cargo efficiently and sustainably, and with the integration of connected and autonomous vehicles. Similar application opportunities occur in areas such as energy, robotics, and autonomous systems, with the common feature of interconnected cooperative and non-cooperative agents interacting via multiple heterogeneous physical and virtual networks. The project will also impact undergraduate and graduate engineering students, and K-12 students through a comprehensive outreach and educational plan that includes STEM camps, engaging activities to promote the recruitment of female students and students from under-served communities and minority schools into the STEM pipeline, and curriculum enhancement initiatives.Traditional decision-making architectures in networked systems and critical infrastructures are grounded on explicit spatio-temporal boundaries between model-based network-level optimization (producing setpoints in a feed-forward fashion) and local closed-loop control (regulating the dynamical system to the setpoints while rejecting disturbances). The modus operandi of these traditional architectures has worked well in settings where the underlying dynamics of the physical systems are slower than the solution time required by network-level optimization tasks, network models and data structures are available, and problem inputs can be pervasively collected in a timely and reliable manner. Such assumptions, however, are becoming increasingly inadequate in dynamic settings where batch approaches fail to solve the underlying optimization problems on a time scale that matches the dynamics of the networked physical systems, physical models (embedded into the optimization task) are difficult to estimate accurately, and (unknown) disturbances evolve rapidly and unpredictably. This project will generate new mathematical principles for the synthesis and analysis of online data-based algorithms that drive the collective behavior of agents and physical dynamics to desired operational points. In particular, the desired equilibrium points coincide with solution trajectories of time-varying optimization problems formalizing performance metrics and operational constraints associated with the dynamical system. The interconnected-system framework under study compresses the time scales between control and optimization tasks to continuously drive the dynamic behavior of physical systems to network-optimal and stable points. The research seeks to expand the class of problems to which this project vision can be applied, develop predictive controllers with information streams, and synthesize novel distributed algorithmic solutions for interconnected systems. The technical approach focuses on networked transportation systems as the arena to materialize the theoretical and algorithmic advances and provide innovative control and optimization strategies. Beyond transportation, benefits are expected to propagate in the broader optimization and control communities, with applications in multiple domains including control of epidemics, robotic networks, social networks, and energy infrastructures.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.