Non-fragile guaranteed cost control for robust spacecraft orbit transfer with small thrust

Abstract

This paper studies the robust orbit transfer problem for low earth orbit spacecraft rendezvous with parameter uncertainties and subject to input constraint and guaranteed cost control. The spacecraft rendezvous process can be divided into in-plane motion and out-of-plane motion because the Clohessy–Wiltshire equations can be decoupled. On this basis, the relative motion models with parameter uncertainties are established. By considering the null controllability with vanishing energy, the problem of orbital transfer control with small thrust and bounded control cost is proposed. Based on Lyapunov theory, a sufficient condition for the existence of the non-fragile robust state feedback controller is given in terms of linear matrix inequalities (LMIs). Then, proper non-fragile controller design can be cast as a convex optimization problem subject to LMI constraints. With the obtained controller, the orbit transfer process can be accomplished with small thrust, where the control cost has an upper bound. An illustrative example is provided to show the effectiveness of the proposed control design method.