Adaptive synchronization of networked Lagrangian systems with irregular communication delays

We consider the synchronization problem of networked Euler-Lagrange systems with unknown parameters. The information flow in the network is represented by a directed communication graph and is subject to unknown and possibly discontinuous time-varying communication delays with unknown upper bounds. We propose a control scheme that achieves position synchronization, i.e., all the positions of the systems converge to a common final position, provided that the directed communication graph contains a spanning tree. The convergence analysis of the proposed scheme is based on the multi-dimensional small-gain framework. Simulation results are presented that confirm the validity of the obtained results.