Adaptive backstepping-based synchronization of uncertain networked Lagrangian systems

In this paper, we study the synchronization problem of networked uncertain Lagrangian systems on directed communication topologies. For the nominal model, we propose a backstepping-based synchronization design for heterogenous Lagrangian systems on digraphs with a spanning tree. We relax the feedback gain constraints on the distributed synchronization control law which encompasses the existing double integrator consensus design as a special case. For the uncertain model, we develop a distributed adaptive redesign assuming that the uncertainty in each agent dynamics can be expressed as a linear parametrization. Simulation results show the effectiveness of the proposed method.