Synchronization of Lagrangian systems with irregular communication delays

Abstract—The synchronization problem of networked Euler-Lagrange systems with unknown parameters is addressed. The information flow in the network is represented by a directed communication graph and is sub-ject 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 con-verge 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 multidimensional small-gain framework. Simula-tion results on a network of ten robot manipulators are given to illustrate the effectiveness of the proposed control scheme. Index Terms—Adaptive control, communication delays, cooperative con-trol, small-gain theorem, synchronization. I