Accelerated consensus in multi-agent networks via memory of local averages

TL;DR

This paper introduces a modified consensus algorithm for multi-agent networks that incorporates memory of previous states, enabling faster convergence and applicability to periodic networks, improving upon classical models.

Contribution

The paper proposes a novel modification to the DeGroot consensus model that uses memory of past states, allowing for accelerated convergence and handling of periodic networks.

Findings

Enables convergence in periodic networks.

Achieves faster consensus than classical models.

Applicable to undirected networks with suitable parameters.

Abstract

Classical mathematical models of information sharing and updating in multi-agent networks use linear operators. In the paradigmatic DeGroot model, agents update their states with linear combinations of their neighbors' current states. In prior work, an accelerated averaging model employing the use of memory has been suggested to accelerate convergence to a consensus state for undirected networks. There, the DeGroot update on the current states is followed by a linear combination with the previous states. We propose a modification where the DeGroot update is applied to the current and previous states and is then followed by a linear combination step. We show that this simple modification applied to undirected networks permits convergence even for periodic networks. Further, it allows for faster convergence than the DeGroot and accelerated averaging models for suitable networks and model parameters.