Formation-Containment Tracking for Heterogeneous Linear Multi-Agent Systems Under Unbounded Distributed Transmission Delays

This paper considers the formation-containment tracking problem of heterogeneous linear multi-agent systems with unbounded distributed transmission delays. The multi-agent system under consideration consists of a reference leader with a desired trajectory, a group of formation-leaders with a prescribed formation, and a group of followers. Novel distributed control laws are proposed for the formation-leaders and followers, respectively. It is shown that under the proposed control laws, the outputs of the formation-leaders not only achieve a prescribed time-varying formation but also track the desired trajectory generated by the reference leader, while the output of each follower converges to the convex hull spanned by the outputs of those formation-leaders. It should be pointed out that many existing results on consensus tracking, formation tracking, and containment control of linear multi-agent systems with constant or bounded distributed transmission delays are included as special cases of our results. Finally, a numerical example is given to illustrate the effectiveness of the proposed controllers.