Distributed containment control of networked nonlinear second-order systems with unknown parameters

In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary / dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders ( regulation case ) and dynamic leaders ( dynamic tracking case ) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders, while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders. Finally, all the theoretical results are illustrated by numerical simulations.