Position and velocity consensus problems of second-order nonlinear multi-agent systems are considered in this thesis. Distributed adaptive controllers are developed to tackle with the uncertain parameters. Introducing new Lyapunov functions, global consensus results are achieved without requiring global Lipschitz condition or polynomiality assumption on the nonlinear functions. As an interesting application and iired from the proposed method for the velocity consensus of general nonlinear systems, a new controller is designed to solve the challenging problem of global frequency synchronization of second-order Kuramoto oscillators with phase shifts. Simulations results demonstrate the effectiveness of proposed method for global frequency synchronization of a network of second-order Kuramoto oscillators with phase shifts.
