Prescribed-Time Formation Bipartite Containment of Layered Multi-agent Systems

This paper aims to address the problem of prescribed-time formation bipartite containment for two-layered MASs (multi-agent systems). In this system, the leader layer engages in a purely cooperative relationship, while the follower layer engages in both cooperation and competition. Moreover, there exists a restraining relationship between the leader layer and corresponding follower layer. By introducing a time-varying function, this paper presents a novel prescribed-time distributed control protocol. The protocol is designed to drive all the leaders to form a formation within a specified time, while the followers simultaneously converge into the convex hulls formed by the states as well as the sign-inverted states of the leaders. Using Lyapunov stability theory, linear matrix inequality, the paper obtains the sufficient conditions for MASs to converge in a specified time and the stability about control algorithm is discussed in detail. Finally, a numerical simulation example is performed to verify the effectiveness of the presented theory.