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

网络正日益成为一个强大的工具，建模和分析自然发生的和工程相互作用的动态系统的属性。 在广泛的应用中，网络动态系统理论提供了一个连贯的框架来建模现象，如高度结构化或同步的全球行为的出现，或分析改变分散的相互作用的动态系统的集合中的自然动态的可能性。 在自然和人造系统中，固有网络结构的存在可以解释集体行为的发生，或者抑制自由控制系统动态的可能性。 虽然这种结构在数学上很罕见，但它们广泛存在于现实世界的网络中，如酵母蛋白质相互作用和人类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，以及社交网络，如电子邮件和学术合作网络。 因此，从控制设计的角度来看，它是必要的，以充分了解一个网络化的动态系统的网络的局部结构如何影响控制或改变其动态行为的能力，并开发算法，避免不必要的控制干预。 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。现有的知识体系之间的关系网络结构和控制多智能体系统的动态的能力已经落后于解决需要控制越来越复杂的网络工程和自然发生的系统。本研究的目的是推进我们的理解，网络多智能体动态系统的拓扑结构如何管理一组代理的选择，以改变整个系统的行为，完成系统级的任务，如状态转移或调节。在拟议的研究中使用的方法将融合技术，从数学控制理论，代数图论和矩阵分析，科学计算。研究成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技术和生物网络中的演示。 预期的结果将添加到一个可用的网络多智能体系统的控制理论的发展。这项研究也将与控制理论和代数图论建立新的联系。 从实践的角度来看，这项研究的影响之一将是提供控制设计工程师和科学家与一个给定的网络的可控性配置文件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.