## 1 Introduction
Second, most BSC systems were designed to be based on the nonlinear model dynamics in each recursive step and are then exposed to the uncertainty issue. Hence, they are sensitive to uncertainties, and control performances will be degraded when the parametric perturbations and external disturbances occur. Further efforts have been made to enforce robustness to uncertainty in the ordinary BSC system. The first solution for the second issue is that BSC is typically combined with the first-order sliding mode control (SMC) [34] by utilizing the robustness property of SMC. However, there is a chattering disadvantage of the first order SMC [35, 36, 37, 38]. As the second solution for the second issue, to enforce control performance by estimating and compensating uncertainties, several disturbance observers are developed [39, 40, 41, 42, 43, 44, 45]. A disturbance observer studied in [39, 40] is applied to estimate uncertainties for nonlinear systems. However, it has the drawback that the observer is designed under the assumption of slow variation of uncertainties. An extended state observer (ESO) in [41, 42] is developed on the position feedback, which is commonly obtained by integrating the velocity information of the system, especially for the multi-rotor UAVs. The long-time integration errors will influence the position information, which further degrade estimation accuracy of the observers. Disturbance observers utilizing a tracking differentiator to bypass the differentiation error in velocity feedback routine are developed in [43, 44, 45]. However, the convergence rate of the state of observer is slow, and the resulting estimation performance for uncertainties is degraded. Hence, to cope with the lower convergence performance in these observers, a more enhanced observer is required to achieve higher estimation and compensation of the uncertainties. Motivated by the aforementioned works, as an alternative to the first-order SMC, the super-twisting algorithm (STA) [46, 47, 48, 49] was developed because the STA offers the following advantages: it requires only the information on the sliding variable; it provides finite-time convergence to the origin for the sliding variable and its derivative; and it generates a continuous control signal to consequently adjust chattering. Furthermore, a novel continuous tracking differentiator based on the sine hyperbolic function is proposed to enhance lower performance traditional tracking differentiators. Finally, a novel disturbance observer based on the proposed tracking differentiator is examined to estimate the external disturbance in USVs. Therefore, in this study, a BSC system combined with STA (SBSC) is considered to realize finite-time convergence and robustness with respect to uncertainty over the conventional BSC system. The contributions of this study are summarized as follows:  
1. The traditional BSC is combined with the STA to enforce insensitivity to variation of uncertainties of a hexacopter UAV system and bypass chattering in the traditional BSC combined with the first-order sliding mode control. 2. The proposed SBSC control strategy for a hexacopter UAV improves finite settling-time convergence when compared to the traditional BSC system. Faster movements of a hexacopter UAV will be expected for a perturbed environmental situation. 3. A novel continuous tracking differentiator based on the sine hyperbolic function is developed to obtain enhanced convergence of the state variable of the tracking differentiator. Thus, faster output of the command filter approximation on the derivative of the virtual control at each recursive step is acquired. The proposed tracking differentiator system exhibits improved performance when compared to the conventional system. 4. An improved nonlinear disturbance observer can be designed by utilizing the proposed tracking differentiator. Hence, the performance of estimation and disturbance rejection for uncertainties of the hexacopter UAV control system are improved by utilizing the proposed disturbance observer.