Bipartite output containment of general linear heterogeneous multi-agent systems on signed digraphs

This study investigates the bipartite output containment control of general linear heterogeneous multi-agent systems on signed communication networks with antagonistic interactions, modelled as negative weights on the digraph. The authors first formulate a new control problem referred to as the bipartite output containment. This control paradigm aims to make each follower's output converge to a dynamic convex hull spanned by the outputs and the sign-inverted outputs of multiple leaders. Second, the authors prove that the bipartite output containment problem can be solved by making some suitably defined signed output containment errors go to zero asymptotically. Then, the authors construct three different control protocols, using full-state feedback, static output-feedback, and dynamic output-feedback designs. These control protocols are based on a distributed feed-forward approach, which requires a feedback gain to make the closed-loop system matrix stable, and a feed-forward gain to drive trajectories of the closed-loop system toward a subspace that renders the regulated signed output containment errors zero. Numerical simulations are performed to validate the proposed control protocols.