Abstract
This paper examines the roles of the matrix weight elements in matrix-weighted consensus. 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.
Highlights
We study how the choice of matrix weights for the inter-agent links affect the presence of clusters in a matrix-weighted graph
The role of each element in the matrix-weights of a multi-agent system has been studied under two classifications: diagonal and non-diagonal elements
With diagonal positive-definite matrix weights, global consensus is guaranteed for each state if the graph is connected at the agent level; otherwise, a similar clustere consensus for each state is achieved
Summary
Our main aim in this paper is to examine how the elements of the matrix-weights W could be chosen, so as to achieve the desired consensus (KCC, GCC, KGC, GC)
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