Consensus with Linear Objective Maps
Abstract
A consensus system is a linear multi-agent system in which agents communicate to reach a so-called consensus state, defined as the average of the initial states of the agents. Consider a more generalized situation in which each agent is given a positive weight and the consensus state is defined as the weighted average of the initial conditions. We characterize in this paper the weighted averages that can be evaluated in a decentralized way by agents communicating over a directed graph. Specifically, we introduce a linear function, called the objective map, that defines the desired final state as a function of the initial states of the agents. We then provide a complete answer to the question of whether there is a decentralized consensus dynamics over a given digraph which converges to the final state specified by an objective map. In particular, we characterize not only the set of objective maps that are feasible for a given digraph, but also the consensus dynamics that implements the objective map. In addition, we present a decentralized algorithm to design the consensus dynamics.
Cite
@article{arxiv.1502.01074,
title = {Consensus with Linear Objective Maps},
author = {Xudong Chen and M. -A. Belabbas and Tamer Basar},
journal= {arXiv preprint arXiv:1502.01074},
year = {2015}
}