Adaptive containment control of coupled linear systems with parameter uncertainties

This paper studies the containment control problem of uncertain multi-agent systems with multiple dynamic leaders by using an adaptive approach. It is assumed that leaders' states are predesigned to be bounded with unknown reference inputs. A new adaptive protocol, based only on the relative states of neighbors, is designed to make the states of the followers converge to the convex hull formed by the multiple leaders. By utilizing tools from non-smooth analysis and matrix theory, it is proved that the followers can asymptotically move into the convex hull if there exists at least one leader that has a directed path to each follower. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.