Optimal feedback guidance with disturbance rejection for endoatmospheric powered descent

An optimal feedback guidance law with disturbance rejection objective is proposed for endoatmospheric powered descent. This guidance law with an affine form is derived by solving a novel problem called Endoatmospheric Powered Descent Guidance with Disturbance Rejection (Endo-PDG-DR). The key idea of formulating the Endo-PDG-DR problem is dividing disturbances into two parts, modeled and unmodeled disturbances: the modeled disturbance is proactively exploited by augmenting it as a new state of a dynamics model; the unmodeled disturbance is reactively attenuated in terms of its effect on the guidance performance by adjoining a parameterized time-varying quadratic performance index in the proposed optimal guidance problem. A Pseudospectral Differential Dynamic Programming (PDDP) method is developed to solve the Endo-PDG-DR problem, and correspondingly a robust neighboring optimal state feedback law is obtained, which has two synergistic functionalities. One is adaptive optimal steering to accommodate the modeled disturbance, and the other is disturbance attenuation to compensate for the state perturbation effect induced by the unmodeled disturbance. Using the derived feedback guidance law, a disturbance rejection level is quantified, and is correspondingly optimized by designing a quadratic weighting parameter tuning law. The numerical computations of interest are performed within a pseudospectral setting, ensuring polynomial analytical solution, high computational efficiency, and reliable convergence.