TY - JOUR
T1 - Distributed averaging with linear objective maps
AU - Chen, Xudong
AU - Belabbas, Mohamed Ali
AU - Başar, Tamer
N1 - Funding Information:
T. Başar was partly supported by the U.S. Air Force Office of Scientific Research (AFOSR) MURI grant FA9550-10-1-0573 ; M.-A. Belabbas was partly supported by NSF ECCS 13-07791 and NSF ECCS CAREER 13-51586 ; X. Chen was supported jointly by (AFOSR) MURI grant FA9550-10-1-0573 and by NSF ECCS CAREER 13-51586 . The material in this paper was partially presented at the 54th IEEE Conference on Decision and Control, December 15–18, 2015, Osaka, Japan. This paper was recommended for publication in revised form by Associate Editor Wei Ren under the direction of Editor Christos G. Cassandras.
Publisher Copyright:
© 2016 Elsevier Ltd. All rights reserved.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - 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.
AB - 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.
KW - Decentralized systems
KW - Distributed averaging
KW - Multi-agent systems
KW - Networked control systems
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U2 - 10.1016/j.automatica.2016.03.023
DO - 10.1016/j.automatica.2016.03.023
M3 - Article
AN - SCOPUS:84963831189
VL - 70
SP - 179
EP - 188
JO - Automatica
JF - Automatica
SN - 0005-1098
ER -