Distributed containment control of second-order multi-agent systems with inherent non-linear dynamics

This study considers the distributed containment control problem of second-order multi-agent systems with inherent non-linear dynamics. Two distributed control protocols with, respectively, static and adaptive control gains are proposed to ensure that the states of the followers asymptotically converge to the convex hull spanned by the corresponding states of the leaders. For the static control protocol, undirected and directed interaction topologies among the followers are taken into consideration, under which sufficient conditions on the control gains are obtained by using a Lyapunov-based approach. For the adaptive control protocol, it is proved that the containment control problem can be solved without requiring any global information if the interaction topology among the followers is undirected. Numerical examples are provided to demonstrate the effectiveness of our theoretical results.