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

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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.