Formation-containment Control for Mutli-agent Systems with Second-order Dynamics and Time-varying Delays

In this paper, formation-containment control problems for multi-agent systems (MASs) with second-order dynamics and time-varying delays are studied. The position and speed of leaders are designed to achieve the time-varying formation and the position and speed of followers are required to enter the convex envelope spanned by those of the leaders simultaneously, which differs from conventional formation control or containment control problems. Using the neighboring positions and velocities, a formation-containment protocol with time-varying delays is considered. By exploiting the space decomposition approach, formation-containment problems are reduced to asymptotically stable problems. Sufficient conditions for second-order MASs with time-varying delays to realize formation-containment are presented. Numerical simulations are shown to demonstrate the feasibility of the theoretical results.