## 5 Further Discussion on the Tracking Control Algorithm
### The Proposed Controller versus Other Control Schemes
[49] proposed an adaptive trajectory tracking control algorithm for unmanned surface vehicles (USVs) with guaranteed transient performance. To make the dynamic USV model more realistic, it was assumed that the mass and damping matrices were not diagonal and the problem of input data saturation was taken into account. Neural networks (NN) were used to approximate the unknown external disturbances and uncertain hydrodynamics of the considered vehicles. The performance of the controller was verified by simulation and experimental studies and compared to the performance of the PI controller. In paper [50], the trajectory tracking problem for underactuated marine vehicles with predefined tracking error constraints was considered. The boundary functions of the predefined constraints were asymmetric and time-varying and allowed for quantitative evaluation of prescribed tracking error performance at both transient and steady-state stages. A novel approach to the control of the transverse function was also developed to introduce an additional control input in backstepping procedure. Due to unmodeled dynamic uncertainties and external disturbances, neural network (NN) approximators were used to estimate uncertain dynamics and disturbance observers. Then, an adaptive control based on NN approximators and disturbance estimators were developed to guarantee the efficiency of error tracking during the transient stage of online NN weight adaptations and disturbance estimates. The simulation results on one vehicle model were compared with model-based control results and showed the effectiveness of the proposed tracking controller. In [52], a practical adaptive sliding mode control scheme for an underactuated unmanned surface vehicle using a neural network, an auxiliary dynamic system, sliding mode control, and backstepping in the presence of modeling uncertainty and input saturation was proposed. A radial basis function neural network with minimum learning parameter method was used for on-line approximation of the uncertain system dynamics. Numerical simulations performed for the CyberShip II model demonstrated the effectiveness of the control strategy. In comparison with sliding mode robust tracking control (known from literature), a reduction of position and velocity tracking errors was obtained (only for circular trajectory). [PERSON] et al. [69] developed a novel event-triggered, complex, real-time learning control strategy for trajectory tracking of underactuated marine surface vehicles considering unknown dynamics and unknown time-varying disturbances. Neural networks (NN) were used to approximate the unknown dynamics. Simulation studies were performed for a vehicle model adopted from the literature. The desired trajectory was circular and two cases with different disturbances were investigated. The controller was effective but its performance was not compared with some other algorithm. Paper [70] addressed the problem of robust finite-time trajectory tracking control for underactuated unmanned surface vehicles (USVs) subject to model uncertainty, saturation constraints, and external disturbances. An output redefinition-based dynamic transformation (ORDT) was utilized and next a sliding mode controller (SMC) was proposed that had the properties of chattering-free and finite time convergence. RBFNN-type neural networks were used to obtain an accurate identification of any continuous function describing unknown parameters of the model and external disturbances. Numerical simulations were performed to demonstrate the validity and effectiveness of the proposed approach. Three different external disturbances were tested on one type of surface vehicle. In [18], the problem of robust tracking of a desired trajectory for underactuated marine vehicles was solved using a finite-time sliding mode control method. The controller design was divided into two stages: the design of the desired velocity and finite-time controller design. A new sliding mode surface was proposed that allowed stabilization of position tracking errors in finite time.