Multi-Agent Edge Controllability Under Matrix Weights
In this paper,the edge controllability of multi-agent systems under ma-trix weights is studied by using the transformation of topological graphs from point graphs to line graphs,where dynamics occur on the edges.Firstly,from the per-spective of graph theory,a quantitative analysis is conducted on the incidence matrix of a line graph,and the relationship between the rank of the incidence matrix of the line graph and the number of connected components of the line graph are given.Furthermore,we find that there is a certain relationship between the algebraic multi-plicity of zero eigenvalues of the Laplacian matrix of the line graph and the number of connected components of the line graph.Secondly,under the leader follower struc-ture model,two conditions that need to be satisfied when the multi-agent system is edge controllable are obtained.In addition,according to the definition of canon-ical transformation,the balanced symbolic line graph of matrix weight structure is transformed into an unsigned line graph without negative edges.The results show that the controllability of the line graph before and after transformation is equivalent.Finally,the relationship between the controllability of line graphs and point graphs is analyzed,and it is found that when the point graph is structurally imbalanced,the controllability of line graphs is equivalent to that of point graphs.
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