## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 179-188 |

Number of pages | 10 |

Journal | Automatica |

Volume | 70 |

DOIs | |

State | Published - Aug 1 2016 |

## Keywords

- Decentralized systems
- Distributed averaging
- Multi-agent systems
- Networked control systems

## ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering