Optimal guaranteed cost control for autonomous rendezvous of spacecraft on elliptical orbit

An optimal guaranteed cost control strategy for autonomous rendezvous operations in a targeted elliptical orbit is presented in this paper. The relative motion equations described by linear Tschauner-Hempel (TH) equations are adopted. Only the relative positions and velocities are available. The real-time orbit elements of the spacecraft in TH equations cannot be estimated because any inertial measurement is unavailable, and then a class of linear low thrust autonomous rendezvous systems with time-varying parameter uncertainties and thrust constraints is modeled. Then, a parametrized representation of a set of guaranteed cost controllers is developed via Linear Matrix Inequalities (LMIs), which can provide thrust acceleration for low thrust autonomous rendezvous. Furthermore, the optimal guaranteed cost controller of low thrust autonomous rendezvous is given which minimizes the guaranteed cost of the closed-loop uncertain system. Numerical results are presented for illustration.