Distributed finite-time containment control for second-order multi-agent systems

This paper addresses the finite-time containment control problem for second-order multi-agent systems under a fixed communication topology. First, a new finite-time consensus protocol based on both the relative position and velocity states is provided for achieving finite-time containment control in multi-agent systems in the presence of multiple active leaders. Then, a finite-time observer-type containment control protocol is exploited, where only the relative position states are involved. By using tools from finite-time control theory, it is theoretically shown that the states of the followers will converge to a convex hull spanned by those of the leaders in finite time, if for each follower there exists at least one leader that has a directed path to that follower. The effectiveness of the results are finally illustrated by numerical simulations.