Finite-Time Containment Control for Nonlinear Second-Order Multiagent System Under Directed Topology

This article investigates the finite-time containment control for a class of second-order multiagent systems with nonlinear dynamics and external disturbances under fixed directed interaction topology. Due to the existence of nonlinear dynamics and unknown but bounded external disturbances, there is an underlying technical difficulty for the design of containment controller. Furthermore, it is a challenge for the theoretical analysis of finite-time containment control problem due to the asymmetric Laplacian matrix arising from the constraint of one-way directed communication among the agents. In response to the above-mentioned challenges, a finite-time containment control algorithm is proposed. First, the multiagent system is considered with inherent nonlinear dynamics and unknown but bounded external disturbances. Second, the desired containment control protocol is presented under a directed interaction topology. Furthermore, by adding a power-integrator technique and Lyapunov function theory, the sufficient conditions are derived for the existence of the finite-time containment controller of a class of second-order multiagent systems. Finally, a numerical example is given to verify the usefulness of the proposed finite-time containment control protocol.