Global leader-following consensus of nonlinear multi-agent systems with unknown control directions and unknown external disturbances

This paper is concerned with the distributed leader-following consensus problem for a class of first-order and second-order Lipschitz nonlinear multi-agent systems with unknown control directions and unknown bounded external disturbances. Moreover, the Lipschitz constant is unknown for controller design and the disturbances are only required to have unknown upper bounds and not necessarily have explicit expression. Some distributed protocols are proposed by using the Nussbaum gain function combing with adaptive control technique. By virtue of algebraic graph theory, Barbalat's lemma and Lyapunov theory and under the assumption that the interconnection topology is undirected and connected, it is proved that the multi-agent systems can achieve global asymptotic consensus even in the presence of external disturbances. Simulation examples are provided to illustrate the effectiveness of the proposed methods.