Non-fragile guaranteed cost control for spacecraft rendezvous

This paper investigates the non-fragile control problem for low earth orbit(LEO) spacecraft rendezvous subjects to the parameter uncertainties, the constraints of small-thrust and guaranteed cost. Based on C-W equations, the relative motion model with parameter uncertainties is established. By considering the null controllability of the model with vanishing energy (NCVE), the non-fragile control design problem with small thrust and bounded control cost is proposed. A sufficient condition for the existence of the non-fragile robust state feedback controller is given in terms of linear matrix inequalities (LMIs) by using Lyapunov theory and LMI technique. Then, proper non-fragile controller design can be cast as a convex optimization problem subject to LMI constraints. With the obtained controller, the spacecraft orbit rendezvous missions can be accomplished successfully, where the control cost has an upper bound. An illustrative example is provided to show the effectiveness of the proposed control design method.