Analysis and Design of the Input-Output Properties of Dynamical Networks

Kasra   Koorehdavoudi

Controllers for many modern networks must be able to achieve increasingly sophisticated functions in a decentralized way under stress and in harsh environments, but also have the opportunity to leverage pervasive cyber systems (including new sensing, communications, and computing technologies) toward this goal. The main idea underlying this dissertation is that such control requires understanding and shaping input-to-output properties of dynamical networks. Based on this motivation, the focus of the dissertation is to: 1) develop graph-theoretic analyses of input-output channels in networks, and 2) understand how built control systems in networks can shape other channels' input-output properties. Toward this aim, we study a sequence of problems on the input-output dynamics (and, specifically, the invariant zeros) of canonical network models, and pursue applications of these methods in real-world settings. As a starting point, we study input-to-output dynamics in a standard linear model for network synchronization or diffusion or consensus, focusing on characterizing the influence of a built controller on the infinite and finite zero structure of a second single-input single-output (SISO) control channel from a graph theoretic perspective. As a further step, we also characterize the finite-zero and infinite-zero structure of a multi-input multi-output (MIMO) channel in the linear diffusive network model. Next, an application on distributed decision-making in the presence of multiple manipulative actors is considered, in the context of this model. In this effort, we evaluate the interplay among the manipulative actors in deciding: 1) the asymptotic decisions reached by the agents and 2) network's transient dynamics. Next, we pursue the analysis of zeros for a more sophisticated network model used in power transmission, namely the classical model for the swing dynamics of the bulk grid; and seek to evaluate the effect of a specific built control (HVDC modulation) on it. We characterize the finite-zero and infinite-zero structure for a SISO channel and investigate the effect of graph topology, input-output location, as well as the type of the control used on the HVDC line. Finally, the design of demand response strategies is pursued, with the aim of modulating the network's operating point so as to achieve desirable small-signal characteristics.

Analysis and Design of the Input-Output Properties of Dynamical Networks

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