Time-Varying Output Formation Containment of General Linear Homogeneous and Heterogeneous Multiagent Systems

This paper investigates the time-varying output formation-containment control of general linear homogeneous and heterogeneous multiagent systems (MAS). This control aims at making each follower's output reach an agreement on the time-varying formation reference, namely, the centroid of the multiple leaders' outputs, and keep a predefined time-varying offset with respect to it. Distributed static output-feedback (OPFB) and dynamic OPFB control protocols are first constructed for homogeneous and heterogeneous MAS, respectively, using only neighboring relative output information and a time-varying formation compensation signal. It is proved that the time-varying output formation-containment problem is solved by making certain output formation-containment errors go to zero asymptotically. Then, local sufficient conditions and explicit local design procedures are provided for both homogeneous and heterogeneous MAS. It is shown that the state/output consensus problems, the state/output containment problems, the state/output formation control problems, the time-varying state/output formation-tracking problems with a single leader, and target enclosing problems of homogeneous/heterogeneous MAS can all be treated as special cases of this paper. Finally, numerical simulations validate the effectiveness of the proposed control protocols.