High Order Optimal Feedback Control of Lunar Landing and Rendezvous Trajectories

Optimal feedback control is classically based on linear approximations, whose accuracy drops off rapidly in highly nonlinear dynamics. A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows the dependency of the spacecraft state on initial conditions and environmental parameters to be represented by high order Taylor polynomials. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems. Based on the reduction of the optimal control problem to an equivalent twopoint boundary value problem, differential algebra is used in this work to compute the high order expansion of the solution of the optimal control problem about a reference trajectory. New optimal control laws for displaced initial states are then obtained by the mere evaluation of polynomials.