Distributed Containment Control for Euler-Lagrange Systems with Dynamic Leaders

This paper considers the distributed containment problem for multiple Euler-Lagrange systems with multiple dynamic leaders in the presence of unknown uncertainties and external disturbances under a directed topology graph. First, we propose a finite-time sliding-mode estimator to obtain accurate estimation of the weighted average of the accelerations, velocities, and positions of the leaders, where each follower can only share its information with its neighbors. Then, we design a distributed adaptive control algorithm combined with finite-time sliding-mode estimators. Furthermore, it is theoretically shown that by using the proposed protocol, the states of the followers will converge to the convex hull spanned by those of the leaders.