Distributed Controllers for Multi-Agent Coordination Via Gradient-Flow Approach

This paper provides a unified solution for a general distributed control problem of multi-agent systems based on the gradient-flow approach. First, a generalized coordination is presented as a control objective which represents a wide range of coordination tasks (e.g., consensus, formation and pattern decision) in a unified manner. Second, a necessary and sufficient condition for the gradient-based controllers to be distributed is derived. It turns out that the notion of clique (i.e., complete subgraph) plays a crucial role to obtain any distributed controllers. Furthermore, all such controllers are explicitly characterized with free design parameters. Third, it is shown how to choose an optimal controller in a systematic way among all distributed ones, where an optimality measure is introduced for the generalized coordination. Finally, the effectiveness of the proposed method is demonstrated through simulations, where a distributed pattern decision is discussed as an example of the generalized coordination.