This paper presents a novel leader-follower formation control for autonomous surface vehicles (ASVs). The dynamic model of ASV and the traditional methods of trajectory tracking are analyzed. Previous research about ASVs' formation focuses on the way of realizing trajectory tracking under conditions, such as time-delays, finite-time, and non-holonomic system. However, principles of constructing a suitable ASVs formation are often neglected. We present a novel leader-follower relation-invariable persistent formation (RIPF) control for ASVs, from which a persistent formation can be generated in any position. Obtained by using RIPF control potential function, the outputs of RIPF control are data points, which should be smoothened using broad learning system (BLS). The global leader navigates the mission trajectory, and each follower follows the RIPF trajectory to satisfy the RIPF potential function. The neural network-based adaptive dynamic surface control is introduced to solve the mission trajectory tracking problems. Environmental disturbances exist in ASV model, and BLS also can be used to approximate the disturbances. The simulation results show that the proposed generative method and control law are effective to realize the desired formation.