Inverse Optimal Stabilization for a Class of Spacecraft Rendezvous Problems

This paper investigates the spacecraft rendezvous problem with target spacecraft in an arbitrary elliptical orbit. The Lawden equations are used to describe the relative motion of two spacecrafts. An inverse optimal method is introduced to deal with the stabilization problem. With Lyapunov analysis, a group of inverse optimal control laws is presented, which guarantees that, the whole system is asymptotically stable, and at the same time, is optimal with respect to a performance index incorporating a positive penalty on the states and the control input. Further- more, a group of modified control laws is obtained, which stabilizes the closed-loop system under input constraints. Simulation results are provided to illustrate the effectiveness of the proposed approach.