## 1 Introduction
The power system of the unmanned aerial vehicle cannot immediately realize such an unrealistic speed change. Employing a fuzzy logic control strategy [19] is a practical solution to address the speed jump issue within the aforementioned backstepping control strategy. Nevertheless, the design of fuzzy logic controllers relies on the designer's prior knowledge, posing challenges in formulating satisfactory fuzzy rules tailored to specific environments. Neural network optimization strategy has been employed as a viable solution for addressing similar issues in unmanned aerial vehicles, enabling the computation of complex nonlinear relationships. However, this approach necessitates online learning training, costly computational resources, and a substantial volume of experimental data. Previous studies have explored the implementation of the backstepping control strategy to achieve position tracking control in quadrotor unmanned aerial vehicles; however, the majority of controller designs overlooked the presence of external disturbances. Previous studies have focused on the development of robust controllers to mitigate the impact of external and internal disturbances on quadrotor unmanned aerial vehicles (UAVs) and ensure stable autonomous flight in challenging environments. One robust control method, the sliding mode control strategy [12], is known for its insensitivity to parameter variance, thereby enhancing the system's resilience to disturbances. However, the control signals generated by the sliding mode control strategy exhibit significant shaking, which can lead to high-frequency variations detrimental to onboard hardware. [PERSON] [20] and [PERSON] [21], expanding on traditional sliding mode control, introduced non-singular terminal sliding mode control methods based on adaptive barrier functions and fast terminal sliding mode control techniques, respectively. These approaches tackle trajectory tracking challenges, particularly in scenarios involving bounded uncertain input constraints, external disturbances, parameter uncertainties, and actuator failures. Both methodologies have demonstrated remarkable effectiveness. While attempts have been made to address the shaking problem in existing methods by substituting the shaking term with saturation and tanh functions [22], these solutions compromise robustness to disturbances and necessitate meticulous parameter tuning to mitigate shaking. Furthermore, given the susceptibility of both backstepping control and sliding mode control to noise, control strategies inspired by biological systems can offer smoother control signals, thus effectively resolving the challenges associated with backstepping control and sliding mode control, which is particularly crucial in the context of limited actuators. Biological neural dynamics, initially proposed by [PERSON] and [PERSON] (1953), refers to the utilization of electrical circuit elements in a patch of membrane within a biological neural system. [PERSON] (1992) introduced these bioinspired neural dynamics to the field of robotics, while [PERSON] (1993) subsequently applied it to the motion control of an underwater unmanned submarine. The overall control design was based on bioinspired neural dynamics and employed a hybrid control approach. A bioinspired backstepping control strategy was employed to address the velocity jump issue in traditional backstepping control, resulting in smooth position control. Additionally, a bioinspired sliding mode control strategy was utilized to tackle the control signal chattering problem in traditional sliding mode control, thereby minimizing the impact on onboard actuators. Therefore, in this paper, a nonlinear hybrid control strategy for quadrotor UAVs aided with the bioinspired neural dynamics model is proposed based on the preliminary work in Refs. ([PERSON] and [PERSON], 2018; [PERSON], 2019; [PERSON], 2019).