# Nonsingular Terminal Sliding Mode Based Finite-Time Dynamic Surface Control for a Quadrotor UAV
## 1 Introduction  
The advantages of Quadrotor Unmanned Aerial Vehicles (UAVs) hare their small size, low energy consumption, and great flexibility. Therefore, they have extensive applications, including environmental monitoring, aerial photography, logistics distribution, and so on. Recently, the quadrotor UAV has been studied extensively. Many scholars have researched control problems regarding the quadrotor UAV, including trajectory tracking control [1], formation control [2], obstacle avoidance control [2], and fault tolerant control [3]. High-accuracy trajectory tracking control is the basis for allowing the quadrotor UAV to complete tasks. Hence, the tracking control trajectory is one of the most important aspects of a quadrotor UAV. However, external disturbances and parameter uncertainties will have negative impacts on the tracking control system. Therefore, studies on the trajectory tracking control problem are becoming increasingly significant for quadrotor UAVs subject to synthetic disturbances [1, 4, 5]. There are many methods to solve the control problem, including sliding mode control (SMC) [6, 7, 8], proportional-integral-derivative (PID) or proportional-derivative (PD) [9] control, adaptive control (AC) [10, 11], backstepping control [12, 13], dynamic surface control (DSC) [14], neural network [15], and model predictive control [16]. Backstepping control is one of the most effective control methods. In [17], a backstepping-technique-based controller was designed for a typical multi-input multi-output (MIMO) system class to address the tracking problem. In [18], an integral backstepping control strategy was proposed for a quadrotor with unknown modeling uncertainties and disturbances to ensure that the system was asymptotically stable. By utilizing the backstepping and fuzzy control techniques, a new sliding mode controller was presented by [19] and used to determine the robustness of the differential wheeled mobile robot. However, backstepping has the disadvantage of leading to an \"explosion of complexity\" after multiple iterations. The DSC technique can overcome this drawback by introducing a filter. The filter can estimatethe derivative of the virtual control law. A DSC-based trajectory tracking controller was designed by [20] for a quadrotor UAV by introducing a first-order low-pass filter. However, the aforementioned scheme did not take into account the estimation error of the filter. In [21], an error compensation signal was designed to compensate for the estimation error. To design a backstepping recursive control scheme for MIMO nonlinear systems, a new finite-time filter was proposed to obtain command signals and their derivatives by [22], where the system was practically finite-time stable. SMC is also one of the most commonly used methods to deal with the tracking control problem. SMC has a history of more than 60 years, and it has the characteristics of simplicity and robustness [23]. SMC has a wide range of applications [24]. However, the bulk of SMC techniques can only ensure asymptotic stability of the system. In order to obtain a fast convergence rate, terminal sliding mode control (TSMC) was developed. In [25], a nonsingular terminal sliding mode control (NTSMC)-based control input was designed to guarantee the fixed-time stability of a second-order nonlinear system. In [26], a continuous integral terminal sliding mode variable was designed to solve the singularity and chattering problems, and the sliding mode variable based control algorithm was proposed to guarantee fixed-time stability of second-order nonlinear systems. To obtain a fast response from the system, a fast terminal sliding mode control (FTSMC)-based controller was designed by [27] for quadrotor UAVs subject to external disturbances and parameter uncertainties. In [28], a FTSMC-based trajectory tracking strategy for autonomous underwater vehicles was proposed to improve the convergence rate.