RUI: Network Structure and Controllability in Natural and Engineered Interacting Dynamic Systems

网络正日益成为建模和分析自然发生和工程交互动态系统特性的强大工具。在广泛的应用中，网络动力系统理论提供了一个连贯的框架来模拟现象，如高度结构化或同步全局行为的出现，或分析在分散的相互作用的动力系统的集合中改变自然动力学的可能性。在自然和人为系统中，固有网络结构的存在可以解释集体行为的开始或抑制自由控制系统动力学的可能性。虽然这样的结构在数学上是罕见的，但它们广泛出现在现实世界的网络中，如酵母蛋白相互作用和人类B细胞遗传网络，技术网络，如美国西部电网，美国机场，互联网和社会网络，如电子邮件和学术合作网络。因此，从控制设计的角度来看，必须充分理解网络动态系统的局部结构如何影响控制或改变其动态行为的能力，并开发避免不良控制干预的算法。拟议的研究将为一所主要为少数民族人口服务的本科院校的学生提供STEM培训。此外，拟议研究的跨学科性质将涉及来自多个STEM学科的学生，如电气工程、应用数学和计算机科学。现有的关于网络结构与控制多智能体系统动态能力之间关系的知识体系，在解决工程和自然发生系统中越来越复杂的网络控制需求方面已经落后。本研究的目的是促进我们对网络多智能体动态系统的拓扑结构如何控制一组智能体的选择以改变整个系统的行为并完成系统级任务（如状态转移或调节）的理解。所提出的研究方法将融合数学控制理论、代数图论和矩阵分析以及科学计算等技术。研究结果将包括与控制给定网络动态系统的能力直接相关的新网络结构目录，以及检测这些结构的有效算法及其在现实世界的技术和生物网络中的演示。预期的结果将有助于网络多智能体系统控制的实用理论的发展。本研究还将与控制论和代数图论建立新的联系。从实际的角度来看，这项研究的影响之一将是为控制设计工程师和科学家提供一个关于给定网络的可控性概况及其对设计分散控制协议的影响的广泛概述。

Networks are increasingly becoming a powerful tool to model and analyze the properties of naturally occurring and engineered interacting dynamic systems. In a wide range of applications, networked dynamical systems theory provides a coherent framework to model phenomena such as the emergence of highly structured or synchronized global behavior, or to analyze the possibility of altering the natural dynamics in a collection of decentralized interacting dynamic systems. In both natural and man-made systems, the presence of inherent network structures may explain the onset of collective behavior or inhibit the possibility of freely controlling the dynamics of the system. Although such structures are mathematically rare, they appear widely in real-world networks such as yeast protein interactions and human B cell genetic networks, technological networks such as the Western States US power grid, US airports, the Internet, and social networks such as email and academic collaboration networks. From a controls design perspective, it is therefore imperative to fully understand for a networked dynamic system how the local structure of the network affects the ability to control or alter its dynamic behavior and to develop algorithms that avoid undesirable control intervention. The proposed research will provide STEM training for students at a primarily undergraduate institution that serves a predominantly minority population. Moreover, the interdisciplinary nature of the proposed research will involve students from several STEM disciplines such as electrical engineering, applied mathematics, and computer science. The existing body of knowledge on the relationship between network structure and the ability to control the dynamics of a multi-agent system has fallen behind in addressing the need to control ever more complex networks in engineering and naturally occurring systems. The objective of this research is to advance our understanding of how the topological structure of a networked multi-agent dynamic system governs the selection of a group of agents to alter the behavior of the overall system and accomplish system-level tasks such as state transfer or regulation. The methods used in the proposed research will blend techniques from mathematical control theory, algebraic graph theory and matrix analysis, and scientific computing. Outcomes of the research will include a catalog of new network structures directly related with the ability to control a given networked dynamic system, and efficient algorithms to detect these structures and their demonstration in real-world technological and biological networks. The expected results will add to the development of a usable theory of the control of networked multi-agent systems. This research will also make new connections with control theory and algebraic graph theory. From a practical standpoint, one of the impacts of this research will be to provide control design engineers and scientists with a broad overview of the controllability profile of a given network and its effect on designing decentralized control protocols.