Inverse optimal design of spacecraft rendezvous problem with disturbances

This paper investigates the stabilization problem of spacecraft rendezvous with target spacecraft in an arbitrary elliptical orbit. A linearized dynamic model, obtained from the Hill-Clohessy-Wiltshire (HCW) equations, is used to describe the relative motion of two spacecrafts. An inverse optimal method is introduced to deal with the stabilization problem in presence of external disturbances. With Lyapunov analysis, A group of inverse optimal control laws is presented, which guarantees the input-to-state stabilization of the whole system, and at the same time, is optimal with respect to a performance index incorporating a penalty on the states, the disturbance acceleration, and the control effort. Simulation results are presented to elucidate the effectiveness of the control strategy.