Satellite formation keeping using robust constrained model predictive control

Numerous controllers have been proposed based on linear Hill\´s equations for satellite formation control. To date, most of these controllers assumed that the system model is well defined, and all the states are known. In this paper, robust constrained model predictive controllers are designed which allows explicit incorporating of the description of parametric uncertainty and the actuator magnitude uncertainty based on this linear Hill\´s equations. The goal is to design, at each time step, a state-feedback control law which minimizes a "worst case" infinite horizon objective function, subject to constraint on the control input. The problem is reduced to a convex optimization involving linear matrix inequalities (LMIs). The proposed robust controllers are evaluated in simulation. The simulation results demonstrate that the proposed controllers are capable of controlling the satellite formation system with parametric uncertainty and the actuator magnitude uncertainty better than LQR