Backstepping-based synchronisation of uncertain networked Lagrangian systems

In this paper, we study the synchronization problem of uncertain networked Lagrangian systems on directed communication topologies. For the nominal model without uncertainties, we propose a backstepping-based synchronization design for heterogenous Lagrangian systems on directed graphs with a spanning tree. We relax earlier constraints on the feedback gain for the distributed synchronization control law, which encompasses the existing double integrator consensus problem as a special case. We then extend the proposed design to the case without relative velocity measurement. For the uncertain Lagrangian model, we develop a distributed adaptive redesign so that the asymptotic synchronization convergence is achieved in the presence of linearly parameterized model uncertainties. Simulation results show the effectiveness of the proposed method.