## 1 Introduction  
In recent years, unmanned aerial vehicles (UAVs) have been used in a broad range of applications that include scientific research, civil engineering, military applications, aerial mapping, search and rescue operations, and risk zone inspections [1]. Quadrotors are an important class of UAVs that has attracted a great deal of attention from scientists and engineers due to their numerous advantages such as rapid maneuverability, diverse applicability, reliability, and economy [2; 3; 4]. However, the quadrotor is a typical example of a coupled underactuated system, as it has six degrees of freedom but only four control inputs. In addition, there are parameterized uncertainties in the quadrotor's rigid body dynamics and aerodynamics which further complicate the design of a high-performance controller. Furthermore, the presence of external disturbances and control input saturation pose a significant challenge to solving the quadrotor's trajectory tracking control (TTC) problem. Meanwhile, the TTC is pivotal to many quadrotor's applications including multi-agent coordination [5], efficient obstacle avoidance [6], and autonomous docking. Therefore, the design of a robust adaptive trajectory tracking controller for quadrotors has become a pressing issue in the scientific community. Several studies have aimed at improving the performance of the quadrotor trajectory tracking control. In [7], the authors proposed a hierarchical flight control scheme using multiple proportional-integral-derivative (PID) controller loops to address the three dimensional (3D) TTC problem. The authors of [8] designed a tracking controller by combining a PID controller and a backstepping controller. The backstepping control technique was also applied in [9; 10] to accomplish the TTC of quadrotors. The \(H_{\infty}\) control method was applied in [11] to solve the output tracking control problem. Another approach was taken in [12], where the authors employed a state space predictive controller to track some predefined trajectories in combination with an \(H_{\infty}\) controller to stabilize the vehicle's rotational movements. In [13; 14], TTC was achieved by applying the sliding mode control (SMC) technique. Yet another tracking controller based on the model-predictive control method was investigated in [15]. Although all the above approaches employ advanced control techniques, they all suffer from the same shortcoming: they all have system parameters and unknown external disturbances that are unaccounted for. To overcome this problem, several quadrotor control methods were investigated such as fuzzy, intelligent control, dynamic surface control, backstepping control, etc. [16; 17]. In [18], the authors presented a novel approximate dynamic programming deep learning algorithm for enabling a quadrotor systems to perform a trajectory tracking in the presence of adversarial inputs. In [19], a neurobiologically inspired intelligent algorithm for quadrotor systems was introduced to achieve the TTC under the presence of uncertain system dynamics and disturbances. Another neural network based intelligent control method was also developed in approach [20] to stabilize a quadrotor system under complex environment including system uncertainties and/or disturbances. These methods [18; 19; 20] can deliver a satisfactory control performance, but require considerable computational resources. Meanwhile, many studies have focused on disturbance-observer (DO)-based tracking controllers to accomplish a robust control performance. Although the authors of [21; 22; 23] investigated backstepping controllers based on a DO and demonstrated good tracking performance, the authors of [24; 25; 26] devised DO-based tracking sliding mode controllers. High gain observers and robust controllers to deal with the tracking problem have also been presented in [27; 28].