Appointed-time formation-containment control for nonlinear multi-agent networks using sample-data feedback

This paper focuses on the single- and second-order nonlinear multi-agent systems, contributing to realizing the formation-containment control over directed communication networks, respectively. By dividing the agents into three types, that is, the tracking-leader, formation-leaders and followers, a class of two-layer sample-data formation-containment control protocols are developed. Then, under the proposed sample mechanism, the investigated problem is transformed into a motion planning problem and the influence caused by non-identical nonlinear dynamics is offset by integral techniques. It shows that with the time projection method, the formation-containment behaviour emerges at an appointed time, which is regardless of any parameters and initial conditions for agents. In comparison with previous results, the main contribution of this paper is achieving the appointed-time formation-containment control and appointed-time tracking to a dynamic leader with nonlinear dynamics. Moreover, the condition on dynamics is more relaxed, only requiring the nonlinearities errors to be bounded. Finally, two simulation examples are given to indicate the effectiveness of obtained results.