Finite-Time and Fixed-Time Bipartite Containment Control of Cooperative-Antagonistic Networks: A unified Framework

This article studies the problems of finite-time and fixed-time bipartite containment control for cooperative-antagonistic networks with multiple leaders over arbitrary weakly connected signed digraphs, in which leaders can be stationary or evolving dynamically through interacting with other leaders in their neighborhood. To this end, a unified distributed nonlinear control scheme is proposed using the nearest neighbor rule. It is shown that under the proposed control scheme, all followers can be guaranteed to converge towards the convex hull formed by each leader's trajectory and its symmetrical one within a finite time or fixed time so long as the underlying weakly connected signed digraph has at least one structurally balanced closed strong component. The efficacy of the proposed control scheme is illustrated via simulations.