Finite-time containment control for multi-agent systems with single-integrator dynamics

In this paper, a novel finite-time containment control framework for multi-agent systems with single-integrator dynamics is established. In such a framework, the multi-agent team can achieve containment control at any preset time, i.e., the followers can move into the convex hull spanned by the leaders at any preset time. In order to reach this goal, linear feedback control protocols with time-varying gains are introduced. Specific functions for time-varying gains are considered and then the result in general form is derived. The proposed preset time dependent time-varying control protocols can solve containment control problems at the preset time if the directed communication topology has a directed spanning forest. Numerical simulations are presented to illustrate the effectiveness of the obtained theoretical results.