Containment control with multiple stationary or dynamic leaders under a directed interaction graph

In this paper, we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under fixed and switching directed network topologies. In the case of stationary leaders, we show necessary and sufficient conditions on the network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in both continuous-time and discrete-time settings. In particular, when the network topology is fixed, the final states of the followers are constant. When the network topology is switching, the final states of the followers might be changing depending on the switching graphs. In the case of dynamic leaders, we propose a distributed tracking control algorithm without velocity measurements and derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states.