## 1 Introduction  
With the development of marine technology, unmanned surface vehicle (USV) has attracted great attention in the field of ocean. This is mainly due to its advantages of being fast, small volume, low cost, and the ability of autonomous navigation. Based on the above advantages, USV has been widely used in many applications, such as oil and gas exploration, ocean surveillance, search, rescue and military [1; 2; 3; 4; 5]. However, the performance of the system is significantly decreased due to the influence of external factors, particularly in the presence of the uncertain system dynamics and external disturbances. Therefore, it is very important to design a controller with the anti-interference capability and higher precision for USV. In recent years, trajectory tracking has been a hot topic of research due to its practical importance. Trajectory tracking is defined as a vessel being required to follow a reference path with spatial and temporal constraint, namely, a reference path with an associated time law [6; 7]. At present, a variety of control schemes associated with trajectory tracking control design for surface vessel have been developed in literature. Global smooth controllers are designed in [8], which achieve the practical stabilization of arbitrary reference trajectories. In [9], a state feedback based backstepping control strategy is proposed, which can enhance the steady state performance and control precision of USV. However, in actual voyage, the model of USV may change due to external disturbances and other factors. In order to overcome this difficulty, an adaptive tracking controller based on backstepping and neural network is developed in [10], in which neural network is hired to handle the unknown dynamics. Based on the sliding mode control and the minimum learning parameter (MLP) technique, an adaptive tracking control scheme is proposed in [11], where dynamical uncertainty and time-varying ocean disturbances are centrally compensated by employing neural network MLP. In addition, for the trajectory tracking problem of the underactuated USV, the biggest challenge is that the number of actuators is less than the degree of freedom, which increases the design difficulty of the controller. Some previous solutions have been published in [12; 13]. A trajectory tracking controller is applied to underactuated surface ships in [12], where the model is represented by numerical methods. Its main advantage is that the calculation of control actions are obtained, solving a system of linear equations. In [13], three modified dynamic inversion methods are proposed to solve the tracking control problem of the underactuated ship, which can remove some of its inherent limitations, making it applicable to a wide variety of underactuated systems. Based on the above analysis, there are still many problems to be solved for tracking control of the underactuated USV. Considering the ship motion control, several authors have contributed a set of novel ideas and strategies. In [14], a robust adaptive control scheme based on modified function projective synchronization is proposed, which can be used in various types of synchronization. Based on dynamic surface control and neural network techniques, a concise adaptive neural network control scheme is proposed in [15]. Its advantage is that the control law has a concise form and is easy to implement, but its disadvantage is that it does not take into account control input hysteresis nonlinearity. In [16], an adaptive fuzzy optimal control method is addressed, which not only guarantees the stability of the system, but also achieves the optimal control performance. With the consideration of robustness, sliding mode control [17] is a successful robust control algorithm, which has been widely used in ship motion control [18; 19; 20; 21], especially in practical engineering. Based on backstepping technique and adaptive dynamical sliding control method, a novel adaptive algorithm is proposed to deal with unknown disturbances and system uncertainties in [22].