## 1 Introduction  
Over the past several decades, quadrotors have seen exciting developments. Their unique advantages have led to broad applications in diverse fields, including post-disaster search and rescue, parcel delivery and environmental monitoring [1]. However, external disturbances can significantly impede the performance of quadrotors [2]. Traditional control methods, such as PID control [3], fail to maintain the ideal performance when the system faces disturbances or model uncertainties. Advanced control methods have been proposed to enhance controller robustness. Adaptive control approaches primarily manage uncertainties and dynamic changes in system models through online parameter adjustments [4; 5]. However, traditional adaptive control methods often require considerable computational resources and must encompass all critical adjustable parameters, which can be a limitation especially for complex quadrotor systems with limited onboard processing power. Incremental nonlinear dynamic inversion (INDI) has demonstrated remarkable robustness against unknown perturbations [6; 7]. The INDI method essentially measures the external disturbances exerted on the system. It then computes the necessary control inputs through inversion of the dynamic model to counter these disturbances. This requires the ability to accurately estimate the dynamic model of the quadrotor, which can pose a significant challenge. Specifically, given that the INDI control law contains the control matrix explicitly, the control performance largely depends on the precision of it. However, existing research does not focus on the inaccuracy of the control matrix, which could lead to performance degradation and even system instability. When dealing with consistently changing disturbances, it is crucial to enable quadrotors to leverage information from previous flights. Learning-based methods can pre-train the control system. However, typical learning-based methods such as reinforcement learning, due to their dependence on extensive data sets and prolonged data processing [8], struggle to meet the real-time requirements of flight control. Additionally, existing learning-based methods often focus on a single environmental condition [9]. Transferring knowledge from previously learned tasks to new tasks under continuously changing environments remains an active area of research [10]. To address these challenges, meta-learning, also known as \"learning to learn\", offers significant advantages [11]. It excels at quickly adapting to fresh challenges by leveraging knowledge from various other tasks. Furthermore, it maximizes the utilization of the limited data, which is particularly beneficial in data-scarc scenarios or situations requiring rapid task adaptation. In this paper, a meta-learning-based INDI control method is proposed to address the adaptation issues of quadrotors in continuously changing environments. The main contributions are as follows: (1)Aiming at decreasing the inaccuracy of the control matrix in INDI, we propose a new method composed of meta-learning and adaptive control. This approach transcends traditional techniques by leveraging the benefits of meta-learning, which equips the system to draw upon prior experiences and adapt more rapidly to unfamiliar and uncertain environments. It not only mitigates the limitations of the traditional adaptive control methods but also enhances the system's ability to deal with dynamic and unpredictable circumstances. (2) We validate a non-asymptotic convergence result, which provides sublinear cumulative control error bounds. Through simulation experiments we show that the proposed control framework possesses a more rapid rate of convergence and a reduced magnitude of error in comparison to the Online Meta-Adaptive Control (OMAC) method [12]. The remainder of the paper is organized as follows. Section 2 introduces the dynamic model with wind disturbances for the quadrotor. Section 3 describes the INDI based trajectory tracking controller.