Periodic Riccati-like differntial equation approach to robust H∞ control of spacecraft rendezvous

This paper investigates the robust H
∞
control problem of spacecraft rendezvous on an elliptical orbit. A new spacecraft rendezvous model is established. On the basis of this model, a robust H
∞
control problem is formulated. A parametric periodic Riccati-like differntial equation approach is used to design a state feedback controller such that the resulting closed-loop system is asymptotically stable, and the H
∞
performance index is minimized under the external disturbance. By an appropriate choice of the value of a parameter, an approximate state feedback controller is obtained from a solution to the periodic Riccati-like differential equation(PRLDE), where the periodic Riccati differential equation is solved based on a new numerical algorithm. With the controller obtained, the spacecraft rendezvous mission can be accomplished successfully. An illustrative example is provided to show the effectiveness of the proposed control design method.