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

This paper considers the finite-time containment control problem for a class of second-order nonlinear multi-agent systems with external disturbances under the directed topology graph. The considered nonlinear systems are composed of multiple dynamic leaders, and they have only a subset of the followers with their accessing to the leaders. Firstly, by using the one-hop neighbors' information, a second-order finite-time distributed observer estimator protocol is constructed to achieve accurate estimation of the weighted average of the velocities and positions of the leaders. Furthermore, it is proved that the proposed estimator protocol can guarantee accurate estimation of the weighted average of the velocities and positions of the leaders in the finite-time. Then, we design a new continuous nonlinear control protocol by means of the nonsingular terminal sliding mode. It is shown that by using proposed control protocol, the states of the followers can converge to the convex hull spanned by those of the leaders in the finite-time. In addition, the finite convergence time can be also explicitly estimated. Finally, the effectiveness of the obtained theoretical results is illustrated by the numerical simulation.