An optimal control approach to robust control of spacecraft rendezvous system on elliptical orbit

In this paper, we propose a new optimal control approach for robust control design of spacecraft rendezvous on elliptical orbit. Lawden equation is used to describe relative motion of the two spacecraft. Based on this equation, a new elliptical spacecraft rendezvous system with parametric uncertainties is established. The control of this typical spacecraft rendezvous system is treated as a robust control problem. The robust control design is then converted to an optimal control design so that both stabilization and performance can be guaranteed. An optimal state-feedback controller is derived by solving Riccati equation, which guarantees the closed-loop system to meet stability and performance requirement. This optimal control approach will not only enhance the system performance but also simplify the design process in that robustness and optimality are integrated in one unified optimal control framework. Furthermore, the obtained controller is simple and easy to implement. The effectiveness of the proposed method is demonstrated by simulation results.