Fixed-Time Quasi-Containment Control with Antagonistic Nodes

This paper investigates the fixed-time quasi-containment control problem of networked multi-agent systems in the presence of antagonistic nodes. Multiple agents are nominated as the leaders, while the remaining agents are the followers. Among the leaders, some of them disseminate not the real state but an opposite one described by scaling parameters. A distributed fixed-time control protocol is proposed to steer the leaders to reach outer-consensus and the followers into the convex hull of leaders' outer states, over the fixed interaction topology. The settling time is estimated and the relationship between control parameters and performance is clarified. Finally, the effectiveness of the algorithm is verified by numerical example.