Fully distributed containment control for second-order nolinear multi-agent systems under a directed graph

In this paper, we study the distributed coordination for second-order nonlinear multi-agent systems with heterogeneous control gains under a general directed graph. The distributed containment problem with multiple dynamic leaders is mainly considered. We first propose control algorithms with heterogeneous constant control gains to ensure all the followers converge to the convex hull spanned by the leaders. It is shown that the constant control gains must be above some positive bounds. We then propose distributed control laws with adaptively updating control gains, which realizes a fully distributed coordination without the need of global information. Furthermore, an adaptive σ-modification scheme is proposed to render smaller control gains and thus requires smaller amplitude on the control input.