Inverse optimal stabilization for spacecraft rendezvous on elliptical orbits

This paper investigates the spacecraft rendezvous problem with the target spacecraft on an arbitrary elliptical orbit. The relative motion of two spacecrafts is established based on the T-H equations. In order to avert some time-varying model parameters, a variable transformation approach is introduced to obtain the new state-space equations. Then, the control laws are designed based on backstepping method. With the analysis by a Lyapunov approach, the proposed control laws can guarantee the asymptotic stability of the closed-loop system and are also optimal with respect to a certain performance index, simulation results are presented to illustrate the effectiveness of the proposed approach.