High order optimal feedback control of space trajectories with bounded control

► The paper describes the fuel-optimal low-thrust transfer problem with bounded control. ► A reference solution for a transfer to the asteroid 1996FG3 is identified. ► An algorithm for expanding the solution in the boundary conditions is presented. ► The algorithm is applied to the high order optimal feedback of the transfer to 1996FG3. ► The algorithm is able to manage a maximum initial and final position error of 10−3 AU.