Optimal Control Laws Considering Controllability Properties in Linear Time/Parameter-Varying Models for Spacecraft Relative Motion in Perturbed Orbits

This paper addresses the optimal feedback control laws for linear time/parameter-varying systems for spacecraft relative motion in perturbed orbits. Although the relative orbit elements are useful representation as relative state variables, coefficient matrix in the linear relative dynamics using relative orbit elements is too sparse and not controllable considering unperturbed relative motion. To avoid such difficulties, linear dynamics considering perturbations is focused on for improving its controllability. Then, two types of linear-quadratic regulator-based controllers considering system’s controllability are proposed and their effectiveness is shown through numerical simulations.