Accelerated Average Consensus Algorithm Using Outdated Feedback

Abstract

This paper examines accelerating the well-known Laplacian average consensus algorithm by breaking its conventional delay-free input into two weighted parts and replacing one of these parts by an outdated feedback. We determine for what weighted sum there exists a range of time delay that leads to increase in the rate of convergence of the algorithm. For such weights, using the Lambert W function, we obtain the rate increasing range of the time delay and also the maximum reachable rate and its corresponding maximizer delay. We also specify what combinations of the current and an outdated feedback increase the rate of convergence without increasing the control effort of the agents. Lastly, we determine the optimum combination of the current and the outdated feedback weights to achieve maximum increase in the rate of convergence without increasing the control effort. We demonstrate our results through a numerical example.