Distributed adaptive coordination for multiple Lagrangian systems under a directed graph without using neighbors’ velocity information

In this paper, we study the distributed coordination problem for multiple Lagrangian systems in the presence of parametric uncertainties under a directed graph without using neighbors’ velocity information in the absence of communication. We consider two cases, namely, the distributed containment control problem with multiple stationary leaders and the leaderless synchronization problem. In both cases, distributed adaptive control algorithms without using neighbors’ velocity information are proposed. The control gains in the algorithms are varying with distributed updating laws. Furthermore, necessary and sufficient conditions on the directed graph are presented, respectively, such that all followers converge to the stationary convex hull spanned by the stationary leaders asymptotically in the containment control problem and the systems synchronize asymptotically in the leaderless synchronization problem. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.