Nonlinear consensus under directed graph via the edge Laplacian

This paper considers a leaderless consensus problem for multi-agent system with inherently nonlinear dynamics under directed graph. To provide an effective perspective to handle the consensus problem, an innovative concept about the edge Laplacian is developed for directed graph. The algebraic properties of the graph Laplacian and edge Laplacian bare a lot in common, and the edge Laplacian has much potential to solve the leaderless consensus problem under the edge agreement framework. By using the proposed consensus protocol, the technical challenges caused by the inherently nonlinear dynamics can be well handled. Finally, the effectiveness of the theoretical results is demonstrated through simulation.