###### Abstract  
This paper investigates the distributed formation control problem of underactuated unmanned surface vehicles (UUSVs) with uncertainties and disturbances and proposes a novel distributed formation controller. The proposed controller redefines the dynamic and kinematic models for each UUSV, which reduces the complexity of the underactuated controller design. Dynamic surface control (DSC) is employed to eliminate the repeated derivatives of the virtual control law, which is crucial for the generation of real-time control signals. The proposed controller integrates neural network approximation with MLP-based adaptive laws to enhance the model's resistance to disturbances. Then, an auxiliary adaptive law is designed for each UUSV to obtain a continuous controller under the compensation of approximate errors and disturbances. The results demonstrate that the controller achieves the desired goals for the formation control, and all control signals are guaranteed to be semi-global uniformly ultimately bounded (SGUUB). The final simulation results thoroughly prove the effectiveness of the theoretical results. U  
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structure. [PERSON] et al. [14] improved the formation control design of a multi-vehicle radial basis function (RBF) neural network by introducing a robust feedback term in the feedback control to compensate for the neural network approximation error and external disturbance, thus obtaining the asymptotic tracking performance of USV formation. [PERSON] et al. [15] proposed an adaptive cooperative control law for USVs based on the adaptive backstepping method to estimate the reference orbiting velocity in bidirectional communication topology, thus eliminating the limitation that every vehicle must obtain the reference trajectory in the existing literature. Aiming at the parametric uncertainty of the USV model, a new adaptive fault-tolerant formation control scheme for USVs with a leader-follower structure was designed, which is suitable for the control of UUSV clusters with a partially known input gain function [16]. [PERSON] et al. [17] provided a multi-vehicle adaptive formation control, which can solve the leader-follower formation problem of UUSV clusters with uncertain dynamics and input constraints. [PERSON] et al. [18] proposed a nonlinear positioning control for the UUSV, which resists unknown disturbance through adaptive heading control. [PERSON] et al. [19] considered UUSV trajectory tracking, provided an optimal control strategy for the vehicle in the presence of external disturbance, and proposed a controller-based model reference adaptive control scheme with an integrator, ensuring the stability of closed-loop systems. [PERSON] et al. [20] considered the trajectory tracking control problem of UUSVs affected by uncertain dynamics and input saturation. This paper uses first-order and second-order sliding mode surfaces to design an underactuated trajectory tracking controller. The auxiliary system solves the potential input saturation problem, uses the MLP method of the neural network to further reduce the computational burden of the controller, and further enhances the robustness of the trajectory tracking system by introducing an adaptive robust term. On this basis, we further studied the distributed formation control problem of UUSVs with uncertainties and disturbances, in which UUSVs can communicate with each other under directed interaction topology. For each UUSV, a new distributed neural network formation controller with two adaptive laws is proposed. First, a virtual control law is established based on static consensus protocol and directed graph theory. Then, the formation controller is derived using DSC, and, then, the adaptive law based on MLP is used to deal with uncertain dynamics. When compensating for approximation errors and external disturbances, auxiliary control laws and corresponding adaptive laws are added to obtain a continuous controller. The main contributions of this paper are summarized as follows:  
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