Inverse optimal adaptive backstepping control for spacecraft rendezvous on elliptical orbits

The spacecraft rendezvous problem with the target spacecraft on an arbitrary elliptical orbit is addressed using adaptive backstepping control. The relative motion of two spacecrafts is established based on the Lawden equations. In order to take the parametric uncertainties into consideration, an adaptive backstepping controller is proposed in this paper, which is optimal with respect to a family of cost functionals. With Lyapunov analysis, the proposed control laws can guarantee the globally asymptotic stability of the whole system and estimate the upper bounds of uncertain model parameters at the same time. Furthermore, a group of modified control laws is obtained, which stabilises the closed-loop system under input constraints. Finally, simulation results are presented to validate the effectiveness of the proposed approach.