Spatial statistical point prediction guidance for heating-rate-limited aeroassisted orbital transfer

• A novel approximate-optimal guidance algorithm for non-linear dynamical systems is presented.
• The guidance algorithm is based on optimal feedback synthesis from a family of extremals.
• Gaussian-process point prediction is utilized for spatial interpolation.
• Extremely fast control computation and low storage requirements suggest suitability for real-time applications.
• Guidance law applicable to high-order systems under path-constraints, currently nearly unsolvable via the HJB equation route.

Feedback control of constrained non-linear dynamical systems satisfying a certain optimality criterion and meeting a specified transfer objective in the state space is recognized as one of the most challenging problems in control theory. One approach to computing optimal feedback policies is the dynamic programming route of numerically solving the Hamilton–Jacobi–Bellman (HJB) partial differential equation directly. In this paper an alternate and more tractable dynamic programming approach, the optimal feedback synthesis method, is utilized. The effectiveness of this 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. This paper presents a solution to the AOTV optimal feedback synthesis problem using the Gaussian process spatial prediction method of universal kriging. A closed-form expression for a near-optimal guidance law is derived. Its performance is found to be very promising; initial atmospheric entry errors due to simulated thruster misfiring are seen to be accurately corrected while the algebraic state-inequality constraint is closely respected.