Finite-time containment control of multi-agent network with nonlinear dynamics

Finite time containment control problem is considered for the second-order multi-agent networks with nonlinear perturbations with bounded norm in the paper. Suppose that there exists at least one leader that has a path to each follower. In the case that the topology between the followers is undirected connected, the control protocol with switching part is designed on the basis of variable structure control idea, moreover, the sufficient condition is obtained to achieve finite time containment control based in matrix theory and finite-time stability principle. When topology between the followers are strong connected, the nonsingular fast terminal sliding mode surface is defined according to network errors, corresponding nonsingular control protocol is designed and the appropriate value range of control parameter is given as to achieve finite time containment control. Simulation examples of two kinds of network topologies are given to verify the correctness and effectiveness of theoretical schemes.