Adaptive synchronization of networked Euler-Lagrange systems under directed graph

The leaderless synchronization of multiple agents modeled by nonlinear Euler-Lagrange equation is investigated under limited directed communication. An adaptive cooperative control law is proposed to synchronize the whole group with parametric uncertainties. It is proved that synchronization can be achieved if and only if the communication graph has a directed spanning tree. Lyapunov theory and eigenvalue-based analysis play key roles in the stability analysis. Robustness to the switching of the communication topology is also discussed. Simulation in the context of attitude coordination of formation flying spacecraft is further conducted to illustrate the effectiveness.