State feedback control for formation keeping in elliptical orbits with unknown relative perturbations

This paper investigates the keeping control for satellite formations in elliptical orbits, in which the relative perturbations between the leader and followers are considered. Firstly, a Type-2 TSK fuzzy logic system (IT2TSKFLS) is adopted to describe the unknown relative perturbations. And the perturbations are estimated by using an adaptive algorithm which is proposed in this paper. Then, in order to achieve a high keeping accuracy, a sliding mode based state feedback controller is developed. The stability analysis is implemented by using Lyapunov theory. Simulation results are presented to demonstrate the effectiveness of the proposed control algorithm.