Containment control for multiple unknown second-order nonlinear systems under a directed graph based on neural networks

In this paper, we first study the distributed containment control problem for multiple second-order nonlinear systems with multiple leaders in the presence of unknown nonlinearities and external disturbances under a directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. We then present a necessary and sufficient condition on leaderless consensus for multiple second-order nonlinear systems with unknown nonlinearities and external disturbances.