Stochastic consensus seeking with measurement noise: Convergence and asymptotic normality

We consider consensus seeking with measurement noise in directed graphs containing a spanning tree. By using stochastic approximation type algorithms, we show the state of each agent converges in mean square and almost surely to the same limit. Furthermore, we show that the approximation error, as the difference between the state vector and its limit, is asymptotically normal after normalization, which in turn characterizes the convergence rate of the algorithm. Finally, we generalize the algorithm to networks with random link failures.