Distributed averaging with linear objective maps

• Xudong Chen ^[1] ; Mohamed-Ali Belabbas ^[1] ; Tamer Başar ^[1]
  1. [1] University of Illinois at Urbana Champaign

     University of Illinois at Urbana Champaign

     Township of Cunningham, Estados Unidos

     
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 70, 2016, págs. 179-188
• Idioma: inglés
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• Resumen

  • A distributed averaging system is a linear multi-agent system in which agents communicate to reach an agreement (or a 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 nonnegative weight and the agreement 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.