## 1 Introduction  
In recent years, cooperative tracking control of multi-UAVs has been developing rapidly for its wide application [1, 2], such as pursuing recovery device in air-recovery [3], following aircraft in a cooperative operation [4] and tracking virtual leader in formation flight [5]. However, there exist many challenges in the research [2]. First, the nonlinear dynamics, in particular the unmodeled dynamics, of UAV make the design of control law more difficult. Second, the disturbance in the environment, such as wind, is to be considered in the coordinated control for the safety of the formation flight.  
For the study of the model of fixed-wing UAV, 6 DOF model [6] is constructed in the early modeling of UAV, where aerodynamic parameters are used to refine the model characteristics. However, it is difficult to be applied in practice due to the coupling characteristics of the model and it is usually used in the maneuver flight with high speed, which relies on the attitude control [7]. To better analyze the movement of UAV in three-dimensional, most researchers adopt 3 DOF model [8, 9] in their study. Furthermore, if the height remains unchanged, the 3 DOF model can be expressed as a unicycle model [10, 11], which is a kinematic model without considering the dynamic characteristics of the UAV. To better analyze the tracking performance of the UAVs in the plane, a 2 DOF model is discussed in this paper based on the assumption that the height of the UAV is constant, which not only preserves the dynamics of the UAV but also simplifies the description of the problem.  
Although most of the models we use are the nominal model, which is a standard model without uncertainties, there is still an uncertain part caused by parameter uncertainties and high-order dynamic terms, which is often difficult to be modeled by functions. Thus, data-driven model is widely used in the model-based control techniques with the development of computer technology. Gaussian process (GF) model is a Bayesian nonparametric regression model, which is widely used in the machine learning [12, 13]. Compared with the neural networks (NNs) [9], GP does not only provide a prediction but also a prediction variance, an effective measure of the uncertainty of the learned model [14]. When model-based methodsare used in control, model errors are of great importance to be taken into account [15]. GP provides uniform error bound [16; 17], while there is no guaranteed bound of the estimation error in NNs [18]. To apply model-based control methods to data-driven models, we use GP regression to model the unknown dynamics of the UAV for its uniform error bound.  
The main contribution of this paper is the design of a cooperative tracking control law for fixed-wing unmanned aerial vehicles based on GP, considering model uncertainty and disturbances. We model the unknown dynamics of fixed-wing UAV based on GP, take the disturbance into account, prove the stability of the system with the help of Lyapunov function and guarantee that the tracking errors are in a certain bound with a high probability.  
The remainder of the paper is as follows: Section 2 reviews the works related to our research. In Section 3, some mathematical symbols are explained, and the basic knowledge of graph theory and Gaussian process regression is introduced. The mathematical description of control problem is established in Section 4 followed by the main results of our work in Section 5, where the learning-based control law for coordinated tracking is proposed and stability with probability for the system is proven. Section 6 shows the results of numerical simulation and demonstrates the effectiveness of the proposed method. Conclusion is drawn in Section 7.