## 5 Conclusions  
In this paper, the SNNC for underactuated formation reconfiguration in elliptical orbit is designed. A linear time-varying dynamical model is used to describe the relative motion of the deputy satellite with respect to the chief. To guarantee trajectory tracking in the presence of thrust failures and unmatched disturbance, the SNNC consisting of the adaptive neural network controller and sliding mode controller is proposed. RBFNN is used to approximate the uncertainty term in the dynamical system and an adaptive law derived via the Lyapunov-based method is used to estimate the upper bound on the approximation error, which avoids the requirement for a priori knowledge of the upper bound on the approximation error and ensures the overall stability of the system. The SNNC, combining the adaptive neural network with adaptive sliding mode work cooperatively, not only improves the control accuracy, but also prevents the adverse effects of inaccurate neural network estimation on the system. The simulation results indicate that the proposed SNNC can obtain higher control accuracy than the LSMC and improve disturbance rejection performance, and the proposed controller could be directly applied to a series of formation reconfiguration missions in the near future. Furthermore, the controller can be adopted in other similar relative orbital control problems, such as spacecraft rendezvous and hovering. The current research focuses on formation reconfiguration in elliptical orbits. In future, we plan to extend our current work in two directions. First, we will extend our work to output feedback control schemes for underactuated spacecraft reconfiguration with the loss of velocity measurements and thrust simultaneously. Second, we will extend our work to similar reconfiguration problems in elliptic orbits using relative orbit elements to reduce the tracking error.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{4}{c}{**Performance Index**} \\ \cline{2-5}  & \(\mathbf{t_{s}}\)**Orbit** & \(\mathbf{d_{s}}\)**, m** & \(\mathbf{\Delta V}\)**, m/s** & \(\mathbf{J}\)**, m2/s3** \\ \hline SNNC & 1.35 & 1.45 & 0.74 & 4.14 \(\times\)\(10^{-4}\) \\ LSMC & 1.46 & 2.17 & 0.74 & 4.14 \(\times\)\(10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Performance indices.  
Figure 9: Trajectories of relative transfer orbit and formation for the case without in-track control.  
**Author Contributions:** [PERSON] supervised the research and reviewed the manuscript. [PERSON] carried out the investigation, methodology, analysis, and wrote the original manuscript. [PERSON] and [PERSON] carried out the simulations, analyzed the results and checked the structure of the paper. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by Young Scientists Fund of the National Natural Science Foundation of China (Grant No: 61906213).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.