## 5 Further Discussion on the Tracking Control Algorithm
### The Proposed Controller versus Other Control Schemes
The results of simulation studies that showed the effectiveness of the control scheme were only for one vehicle model (with a mass of about 2 kg) and were not compared with the results of another algorithm. [PERSON] et al. [27] proposed a sliding mode controller to solve the problem of trajectory tracking of an underactuated surface vessel. By combining adaptive continuous sliding mode control with a backstepping method, the chattering phenomenon reducing and the trajectory tracking problem were successfully solved. Moreover, a novel sliding mode PI control was designed, which made the control scheme more practical. In the simulation studies, one marine vehicle model was tested and for one complex desired trajectory. The control algorithm was found to be effective in the trajectory tracking task, but its effectiveness was not compared in the simulations with that of another controller. The control problem of tracking the trajectory of underactuated surface vessels using a quantitative method with only position and attitude available was considered in [41]. Using a combination of a high-gain observer, a parameter compression algorithm, and a performance function, an adaptive control strategy with a given performance was presented. A high-gain observer was constructed for velocity estimation, and the parameter compression algorithm was used to account for persistent perturbations and model uncertainties in a more concise manner. The controller guaranteed the prescribed performance. Numerical simulations were performed for one ship model (taken from the literature) and one desired trajectory. The control scheme proved to be effective and slightly smaller trajectory tracking errors were obtained compared to another tested algorithm. [PERSON] et al. [42] developed a novel robust adaptive control scheme for trajectory tracking with prescribed performance for autonomous underwater vehicles in horizontal motion subject to unknown dynamic parameters and disturbances. A simple error mapping function was proposed to ensure that the trajectory tracking error meets the prescribed performance. In addition, a novel control based on the Nussbaum function was added to deal with the underactuation of the marine vehicle. The simulations presented were for one vehicle, tracking a desired sinusoidal trajectory for two different disturbances functions. In both cases, the controller worked correctly and was effective. In [71], a new adaptive performance control (PPC) strategy was presented for a class of USVs when parametric uncertainty and external disturbances were present. Prescribed performance and steady-state performance in terms of trajectory tracking velocity and accuracy were achieved using continuous and singularity-free control. In addition, the controller eliminated the need for disturbance observers and the assumption that disturbances must be differentiable. A simulation study performed on one ship model confirmed the effectiveness of the controller. It also turned out that the offered approach outperformsin terms of tracking performance (less error perturbation) the method selected from the literature for comparison. [PERSON] and [PERSON] [72] proposed a robust control methodology based on to track the trajectories of uncertain USVs under the presence of external disturbances in a band-limited network environment. They used a coordinate transformation method and an auxiliary signal to solve the problem of insufficient activation of a USV model (with asymmetric stern and bow). They assumed that all USV states and inputs are quantized by a uniform quantizer, which was designed using a low-complexity PPC method. The proposed quantized feedback tracking system consisted of performance functions and error surfaces using quantized states, which did not require any adaptive techniques. Conditions for the selection of the performance functions were also given. Simulation results shown that the proposed control strategy was effective for the control problem under a band-limited network with state and input quantization.