H∞ Time-Varying Group Formation-Containment Tracking Control of Multi-Agent System With Multiple Leaders

The $H_{\infty } $ time-varying group formation-containment tracking (TVGFCT) problem of multi-agent system (MAS) with multiple leaders is investigated in this paper. The MAS is assumed to be composed of multiple tracking leaders, formation leaders and followers and all the agents are divided into different groups. Firstly, based on the relative information, the distributed observers for the formation leaders are designed to estimate the convex combination of tracking leaders in the same group. Then the observer-based $H_{\infty } $ time-varying formation tracking protocols are proposed to make the formation leaders realize the desired time-varying formation while tracking the convex combination of tracking leaders, and an algorithm to construct the protocols is given. Then the containment tracking protocols are designed and the sufficient conditions to ensure the effectiveness of the proposed protocols are presented, and the algorithm to construct the containment tracking protocols is also given. Finally, the simulation results illustrate that when there exist external disturbances, the designed formation-containment protocols can make the MAS realize $H_{\infty } $ TVGFCT.