Backstepping-based synchronized tracking control for networked uncertain Lagrangian systems under a directed graph

This paper investigates the backstepping-based distributed tracking control problem for multiple Lagrangian systems with linearly parameterized model uncertainties under the directed communication topology with a directed spanning tree. We consider the dynamic leader case. The leader information is available to only a subset of the followers. By using the position errors of the neighbors as the reference signals, an adaptive design method is given for each follower. Rigid theoretical proof is presented for the proposed scheme with backstepping technology with three steps. It is shown that the tracking errors of each follower are bounded. Simulation results are provided to illustrate the effectiveness of the proposed control algorithm.