#### Xiaochuan Zhao 2014

Abstract of PhD Dissertation
Electrical Engineering Department, UCLA, September 2014
One key challenge in real applications is that networked agents generally face many types of asynchronous imperfections, such as random link failures, random data arrival times, noisy links, random topology changes, agents turning on and off randomly, and even drifting objectives. This dissertation provides a detailed analysis of the stability and performance of asynchronous diffusion strategies for solving distributed optimization and adaptation problems over networks in the presence of such imperfections. Conditions are developed to ensure the stability of the mean-square and mean-fourth-order moments of the network error vectors; closed-form expressions are derived to reveal how the network parameters influence the learning behavior; and the performance of the asynchronous networks is then compared against centralized solutions and synchronous networks. One notable conclusion is that the mean-square performance of asynchronous networks degrades only in the order of $\nu$, which is a small step-size parameter, while the convergence rate remains largely unaltered. A second notable conclusion is that even under the influence of asynchronous events, all agents in the adaptive network can still reach an $O(\mu^{1+\gamma})$ near-agreement with some constant $\gamma > 0$, while approaching the desired solution within $O(\mu)$ accuracy. These theoretical results provide a solid justification for the remarkable resilience of cooperative networks in the face of random imperfections at multiple levels: agents, links, data arrivals, and topology.