## 1 Introduction  
Spacecraft formation flight is rapidly becoming a hot topic of research in space with its great potential for Earth observation, in-orbit services, deep space imaging and exploration [1, 2, 3]. It decentralizes the functions of a single spacecraft into a group of smaller ones, thereby reducing risk and cost and improving reliability and adaptability [4]. The ability of these spacecrafts to reshape or retarget from one formation to another completes the formation reconfiguration, greatly increasing the flexibility of formation missions. The methods of formation reconfiguration using continuous thrust can generally be divided into two categories: fully actuated and underactuated. Fully actuated means that there are independent control channels in the radial, in-track and normal directions. The current research on consensus with formation reconfiguration focuses on fully-actuated systems, a series of control methods have been proposed for the full-actuated formation reconfiguration mission such as sliding mode control, state Riccati equations, adaptive control, and neural network control [5, 6, 7]. If the thrusters break down in one direction, the number of independent controls of the system is less than the degrees of freedom, it becomes an underactuated system, which cannot complete the reconfiguration mission, and the above control schemes are then not applicable anymore. Although the installation of backup thrusters can solve this problem, considering the need for light weight and miniaturization of spacecraft in the future, it is more economical and effective to design an underactuated control scheme. Focusing on the fully actuated reconfiguration problems, scholars at home and abroad have conducted much research, but seldom have works that deal with the underactuated reconfiguration been reported in the literature. [PERSON] et al. examined the feasibility of formation control using only in-track differential atmospheric drag [8] and a linear feedback controller for underactuated formation reconfiguration was designed by [PERSON] et al. [9]. [PERSON] et al. designed a nonlinear controller for formation reconfiguration without in-track thrust [10]. [PERSON] et al. designed an impulsive control strategy for the elliptical relative motion based on the relative orbit elements [11]. [PERSON] et al. derived the optimal analytical solution for an underactuated formation reconfiguration in circular orbits and proposed an underactuated controller for formation reconfiguration in elliptical orbits [12,13]. [PERSON] proposed the control scheme to achieve the optimal formation reconfiguration with bounded and small attitude changes using only a few thrusters [14]. The traditional formation reconfiguration control adopts the linearized CW equations [15] or Tschauner-Hempel equations [16] to model the relative motion of the satellites within the formation and ignores the external perturbation [17,18]. To overcome this requirement, neural networks are capable of approximating arbitrary smooth functions on tight sets with arbitrary accuracy and are therefore widely used to estimate nonlinear uncertainties in system dynamics. Despite the ability to approximate with high accuracy, approximation errors still exist. As a result, in most previous work [19,20,21], it was only possible to guarantee that the state error was consistently and eventually bounded, or that it was arbitrarily small if the feedback gain [22] was sufficiently large. Neural network-based controllers need to add more nodes when the application range increases in order to meet the higher accuracy, which leads to a complex structure and too much computation for real-time in-orbit calculations. Inaccurate estimation of the neural network will also affect the performance of the whole controller and even cause the system to diverge. To address such issues, [PERSON] et al.