Neighboring optimal trajectories for aeroassisted orbital transfer under uncertainties

A neighboring optimal guidance scheme is presented for a nonlinear dynamic system in the presence of modeling and measurement uncertainties as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. Here the vehicle is expected to follow a desired reference path with minimum error. The measurements considered include tracking of altitude and altitude rate. The solution approach is based on nonlinear control optimization, deterministic perturbation, stochastic state estimation, and linearized stochastic control that leads to a closed-loop control law. The reference state trajectory and control trajectory are precomputed by solving a two-point boundary-value control problem. Numerical results show that the actual (true) state trajectory is kept near its ideal (reference) state trajectory at the expense of increasing the total cost. (Author)