Containment control with multiple interacting leaders under switching topologies

In this paper, containment control for continuous-time multi-agent systems with multiple interacting leaders is investigated. According to the role each agent plays in the multi-agent team, the agents are classified into two categories: leaders and followers. The containment control problem in this paper is that the leaders converge to a desired formation and the followers move into the convex hull spanned by the leaders' final positions. A sufficient condition for containment control is that the union of the interaction graphs has a spanning tree frequently enough as the system evolves. It is shown that the followers' positions in the convex hull are dynamic due to the switching topology. The theoretical results are illustrated by some simulations.