Adaptive Filter Algorithms for Accelerated Discrete-time Consensus

In many distributed systems, the objective is to reach agreement on values acquired by the nodes in a network. A common approach to solve such problems is the iterative, weighted linear combination of those values to which each node has access. Methods to compute appropriate weights have been extensively studied, but the resulting iterative algorithms still require many iterations to provide a fairly good estimate of the consensus value. In this study we show that a good estimate of the consensus value can be obtained with few iterations of conventional consensus algorithms by filtering the output of each node with set-theoretic adaptive filters. We use the adaptive projected subgradient method to derive a set-theoretic filter requiring only local information available to each node and being robust to topology changes and erroneous information about the network. Numerical simulations show the good performance of the proposed method.