Graph-theoretic methods for the analysis and synthesis of networked dynamic systems

Graph-theoretic Methods for the Analysis and Synthesis of Networked Dynamic Systems Daniel Zelazo Chair of the Supervisory Committee: Professor Mehran Mesbahi Aeronautics & Astronautics This dissertation aims to develop a graph-centric framework for the analysis and synthesis of certain classes of large-scale systems, namely, those with linear dynamic subsystems that interact with other subsystems via an interconnection topology. Four canonical models for networked dynamic systems (NDS) are derived as the analytic foundation for this work. The role of heterogeneity of the agent dynamics comprising the system is also made explicit. An essential construct used to describe these systems is a new algebraic representation for a graph that we term the edge Laplacian. Equipped with models that explicitly describe the role of the underlying connection topology, we consider the controllability, observability, and performance of the NDS models in terms of the structural properties of the connection graph. Motivated by the analysis results, we also provide various synthesis procedures, including optimal topology design, local inner-loop control for each agent in an NDS, and decentralized control laws for the entire NDS.

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