Distributed control of networked multi-agent systems for high-dimensional coordination

In this paper, we characterize a network structure which enables us to achieve a high-dimensional coordination by distributed control of networked multi-agent systems. The high-dimensional coordination is a control task which contains free parameters determined by agents themselves. We derive necessary and sufficient conditions of graphs with which the high-dimensional coordination is achievable in both a geometric form and an algebraic one. Finally, a numerical example illustrates the validity of the obtained analysis.