Consensus Over Networked Dynamical Systems: Control, Design, & Interaction

Abstract

This dissertation focuses on three main aspects of control theory applied to networked dynamical systems -- how to control networked systems, how to design networks to facilitate control and estimation for such systems, and how to reason about interacting with them. We examine how network symmetries and how the distribution of cooperative and antagonistic interactions facilitate control of the seminal consensus protocol, as well as measures that indicate how well a network facilitates consensus. Various tools for designing complex networks are developed in this dissertation, including decentralized update schemes for improving network edge weights and the time scales on which the agents in the network operate. The crux of the analysis of these algorithms lies in a beautiful connection between electrical network theory, the paradigm of series-parallel networks, and multi-agent consensus. Lastly, we examine how to design feedforward and feedback controllers for consensus networks that have state-dependent edge switching. The key tool is a continuum approximation of the agent dynamics, which allows for an optimal transport approach for feedforward control, and a density gradient feedback scheme.