Fixed-time ILF observer-control scheme for spacecraft rendezvous

In this paper, the problem of fixed-time control for spacecraft rendezvous on elliptical orbit is addressed based on implicit Lyapunov function (ILF) method. In view of uncertain parameters and external disturbances, an observer-control scheme is introduced, where the controller and the observer are proved fixed-time stable, respectively. The corresponding gains are obtained by solving linear matrix inequalities (LMIs) or parameterized nonlinear matrix inequalities (NLMIs), and the analytical solutions to these matrix inequalities are provided to reduce the computational burden. The effectiveness of the theoretical results is demonstrated by simulation examples.