Formation-containment control for second-order multi-agent systems with time-varying delays

In this paper, formation-containment control problems for multi-agent systems with second-order dynamics and time-varying delays are studied. The states of leaders are designed to achieve the time-varying formation and the states of followers are required to converge to the convex hull spanned by those of leaders simultaneously, which differs from conventional formation control or containment control problems. Using the neighboring positions and velocities, formation-containment protocols with time-varying delays are constructed. By exploiting the space decomposition approach, formation-containment problems are transformed into the asymptotically stable problems. Sufficient conditions for second-order multi-agent systems with time-varying delays to realize formation-containment are presented. A method to obtain the unknown gain matrices in the protocols is proposed. Numerical simulations are shown to illustrate the effectiveness of the theoretical results.