Centralized and decentralized formation control with controllable interaction laws

In this paper, we will consider a formation control model whereby the multi-agent system is governed by a set of controllable interactions between pairs of agents, and a connected, undirected graph is used to specify selected interactions that are under control. We investigate the control model from two perspectives: one is from the view of classic control theory while the other is from the view of decentralized formation control. We show that the model, when treated as a centralized control system, is approximately path-controllable. We establish this result by identifying the control model with a related control-affine system, and then verifying the Lie algebra rank condition. After that, we look into the control model as a decentralized control system. A particular pattern of information flow will be considered and a decentralized solution that relates to a gradient-like flow will be investigated in detail.