Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

ON THE ROLE OF MATRIX-WEIGHTS ELEMENTS IN CONSENSUS ALGORITHMS FOR MULTI-AGENT SYSTEMS

Version 1 : Received: 20 August 2021 / Approved: 23 August 2021 / Online: 23 August 2021 (14:48:25 CEST)

A peer-reviewed article of this Preprint also exists.

Ogbebor, J.; Meng, X. On the Role of Matrix-Weights Elements in Consensus Algorithms for Multi-Agent Systems. Network 2021, 1, 233-246. Ogbebor, J.; Meng, X. On the Role of Matrix-Weights Elements in Consensus Algorithms for Multi-Agent Systems. Network 2021, 1, 233-246.

Journal reference: Network 2021, 1, 14
DOI: 10.3390/network1030014

Abstract

This paper extends the concept of weighted graphs to matrix weighted graphs. The consensus algorithms dictate that all agents reach consensus when the weighted graph is connected. However, it is not always the case for matrix weighted graphs. The conditions leading to different types of consensus have been extensively analysed based on the properties of matrix-weighted Laplacians and graph theoretic methods. However, in practice, there is concern on how to pick matrix-weights to achieve some desired consensus, or how the change of elements in matrix weights affects the consensus algorithm. By selecting the elements in the matrix weights, different clusters may be possible. In this paper, we map the roles of the elements of the matrix weights in the systems consensus algorithm. We explore the choice of matrix weights to achieve different types of consensus and clustering. Our results are demonstrated on a network of three agents where each agent has three states.

Keywords

matrix-weighted graphs; multi-agent systems; clustered consensus; global consensus

Subject

ENGINEERING, Electrical & Electronic Engineering

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