Distributed synchronized tracking control of Euler-Lagrange systems on directed graphs

This paper is concerned with the distributed synchronization tracking control problem of multiple Euler-Lagrange systems on a directed graph which contains a spanning tree with the leader node being the root node. Compared to the case of undirected communication graph, the problem is more challenging since the Laplacian matrix of the communication graph is asymmetric such that it is not easy to use the `skew-symmetric´ property of the Euler-Lagrange systems for stability analysis. In each agent, a local controller is designed with the disturbance observers and sliding mode control terms to suppress the mutual interactions among the agents and the modelling uncertainties. The conditions for guaranteed control performance are clarified and a simulation example demonstrates the performance of the distributed controllers.