Mean-square optimal weight design for average consensus

In this work we investigate the best possible convergence of average consensus in the mean-square sense with weights that change over time. Although this convergence may be hard to achieve in practice, it provides useful practical insights into the behavior of average consensus. In particular, we show that the correlation between the states plays an important role in the design of the weights and that the weight-morphing scheme proposed in our previous work is close to optimal both for correlated and uncorrelated measurements.