This paper investigatesthe prescribedtime bipartite formation-containment tracking control for the layered multi-agent systems (MASs) under the signed digraphsbased on the observer. In this system, the leader layer track the trajectory of the tracking leader and 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, a distributed prescribedtime observer is designed for the leader layer to accuratelyestimation of the tracking leader’s state within the prescribed time. A novel prescribedtime distributed control protocol is designed to drive leader layer to approach the tracking leader and form a formation within a prescribed time, while the follower layer simultaneously converges into the convex hulls formed by the states and the sign-inverted states of the leader layer. By using graph theory and Lyapunov stability theory, the validity of the designed control protocol is proved in detail, and the corresponding sufficient conditions for the prescribed time stability of the MASs are derived. Finally, a simulation example confirms the effectiveness of the analytical results.
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