Near-optimal feedback guidance for aeroassisted orbital transfer via spatial statistical prediction

Feedback control of constrained non-linear dynamical systems satisfying a certain optimality criterion and meeting a specified transfer objective in the state space is well recognized as one of the most challenging problems in control theory. One approach to computing optimal feedback policies is the well-known dynamic programming route of numerically solving the notoriously difficult Hamilton-Jacobi-Bellman partial differential equation directly. In this paper, the effectiveness of a new implementation of an alternate, and more tractable dynamic programming approach, the optimal feedback synthesis method, is demonstrated through an explicit guidance scheme for the heating-rate-constrained maneuver of an Aeroassisted Transfer Vehicle (AOTV). In optimal feedback synthesis, a feedback chart is constructed from a family of open-loop extremals, thus ensuring optimality with respect to any initial condition in the family. In this work, a solution to the AOTV optimal feedback synthesis problem is proposed using the Gaussian process spatial prediction method of universal kriging. A closed-form expression for the guidance law is derived, the performance of which is found to be very promising; initial atmospheric-entry errors due to simulated thruster misfiring are seen to be accurately corrected while closely respecting the algebraic state-inequality constraint.