Disturbance Propagation in Dynamical Networks by Subir Sarker – Final Exam

About the event

Student: Subir Sarker

Advisor: Dr. Sandip Roy

Degree: Electrical and Computer Engineering, Ph.D.

Dissertation Title: Disturbance Propagation in Dynamical Networks

Abstract: Analysis and control of the propagation of disturbances in dynamical networks are the focus of this dissertation. Specifically, we use graph-theoretic analysis to characterize the disturbance responses in sparsely actuated and sensed dynamical networks. In addition, we define the stability of disturbance propagation in general dynamical networks and investigate it in inverter-based microgrids. In general, the dissertation addresses three distinct but interconnected research problems. First, we consider the input-output analysis of a discrete-time linear network synchronization model using graph-theoretical analysis. We demonstrate that some input-output metrics, including gains, frequency responses, frequency-band energy, and Markov parameters, show a spatial decrescence property that is nonincreasing along separating cutsets away from the disturbance source. The spatial analysis is then extended to a class of nonlinear dynamical systems, the self-confidence dynamics of the modified DeGroot-Friedkin model for opinion formation in networks. Second, motivated by the spatial analysis of dynamical networks, we consider disturbance propagation stability notions for a synchronization process of homogeneous subsystems coupled linearly and droop-controlled microgrids. Here, we present a general definition of disturbance propagation stability based on the degradation of response norms with separating cutsets away from the disturbance source for both models. Using the definition, we then characterize the disturbance propagation stability of these models in terms their parameters. Third, the structural controllability of a droop-controlled microgrid is analyzed using graph-theoretic analysis. We demonstrate that the microgrid model is structurally controllable for input at the digraph’s zero-forcing sets (a graph-theoretic property) and verify the result in two test systems.