Distributed containment control for multiple nonlinear systems with identical dynamics

In this paper, we study the distributed containment control problem for multiple nonlinear systems with multiple dynamic leaders. The objective is that a team of followers converges to the convex hull spanned by multiple dynamic leaders with identical dynamics as the followers. The strategy has many applications such as securing a group of followers in the area spanned by the leaders so that they can be away from dangerous sources outside the area. We first propose a control algorithm to achieve the objective under a directed graph. To compensate the drawback that the control gain of the control algorithm under a directed graph has a lower bound depending on the Laplacian matrix, we then propose an adaptive control gain design using only local information of the followers´ neighbors. Therefore, the proposed control algorithm for the containment control problem is totally distributed under the condition that the interaction among the followers is undirected. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.