Aiming at the trajectory tracking control of
　　underactuated vessels with parameters uncertain and
　　external disturbance
　　problems, a stable adaptive neural network control
　　method is proposed. Based on the diffeomorphism
　　transformation, the new
　　tracking variables are given. First, the kinematics
　　controller is designed to track the new variables and
　　the velocity command is
　　proposed. Second, the dynamics controller using
　　neural network method is designed to make the real
　　velocity of the underactuated
　　surface vessel reach the desired velocity command.
　　All the parameters update laws are selected in terms
　　of Lyapunov functions,
　　which guarantee the closed-loop systems to be
　　uniformly ultimately bounded (UUB). Finally, a
　　numerical simulation illustrates the
　　effectiveness of the proposed control method.