Title: Stochastic Approximation for Consensus: Asynchronous Algorithms and Mean Square Convergence (1 hour)
Abstract: This work considers consensus problems with delayed noisy measurements in switching networks, and stochastic approximation algorithms are applied. A major challenge is that the popular quadratic Lyapunov function based approach cannot be applied to prove convergence. The main contributions of this work include the analysis of backward products of degenerating stochastic matrices and subsequently the proof of mean square consensus. The ergodicity results for the stochastic matrices are obtained via a discrete time dynamical system approach and are different from the traditional ergodic coefficient based approach.