CAREER: Graphs, geometry and algorithms for sparse decentralized control systems

目的：近年来，一种新的控制系统范式已经出现，现在越来越多地被视为相互作用的自主智能体的集合。分散的电力分配系统、用于援助甚至包裹递送的无人自动驾驶车辆的形成、地面车辆排和拍卖系统都是围绕这一新模式建立的控制系统。同样，生物科学的进步，以及提供全面和负担得起的医疗保健的需要，使得绘制复杂的遗传、代谢和最近的疾病网络图变得司空见惯。智力优势：这项研究涉及一种新的框架，它结合了图论、计算机科学和动力系统的思想。重点放在控制理论方法上，这些方法足够广泛，可以解决各种应用环境中出现的相关问题，但又足够具体，可以产生可实现的方法和算法。具体问题包括：如何刻画完成任务所需的最小通信结构(哪些链路是协同工作所必需的，哪些链路是冗余的？)，如何量化网络对攻击和链路故障的抵抗力(什么是健壮性的良好衡量标准？)，如何构建完成给定任务的网络(什么是最经济的网络设计？)。广泛影响：本文提出的工作将为大规模、安全和高效的多代理系统的部署和分析提供关键技术。在过去的二十年里，集中控制系统的范例已经逐渐消失，取而代之的是大规模的、异类的、有时是临时的和分散的系统。由于所提出的框架直接将动力学与底层网络联系起来，其潜在的应用跨越了网络动力学出现的各个子领域，包括但不限于分布式优化、新陈代谢网络的研究、队形控制和分散的功率分配。

Objective: In recent years, a new paradigm for control systems, now increasingly seen as a collection of interacting autonomous agents, has emerged. A decentralized power distribution system, a formation of unmanned autonomous vehicles used for aid or even package delivery, terrestrial vehicles platoons, and auctions systems are all control systems built around this new paradigm. Similarly, progress in the biological sciences and the need to provide comprehensive and affordable healthcare have made the mapping of complex genetic, metabolic and more recently disease networks commonplace. Intellectual merit: The research deals with a novel framework that unites ideas from graph theory, computer science and dynamical systems. The focus is on control-theoretic methods that are broad enough to address the relevant questions arising in various application settings, yet specific enough to yield implementable methods and algorithms. Specific questions include: how to characterize the minimal communication structure needed to accomplish a task (which links are necessary for the ensemble to cooperate, and which ones are redundant?), how to quantify the resistance of a network to attacks and link failures (what is a good measure of robustness?), how to construct networks accomplishing a given task (what is the most economical network design?).Broader Impacts: The work proposed here will provide key technologies to enable the deployment and analysis of large-scale, secure and efficient multi-agent systems. Over the course of the past twenty years, the paradigm of centralized control systems has faded in favor of systems that are large-scale, heterogeneous, sometimes ad-hoc, and decentralized. Because the proposed framework directly relates the dynamics to the underlying network, its potential applications span the various subfields where networked dynamics appear, including, but not limited to, distributed optimization, the study of metabolic networks, formation control, and decentralized power distribution.