Using sensitivity penalties to robustify the optimal reentry trajectory of a hypersonic vehicle

In the paper at hand, an optimal reentry trajectory for a winged hypersonic vehicle is calculated, where the maximum heat flux at the stagnation point is minimized. The main contribution of this paper is the robustification of the optimal reentry trajectory against air density fluctuations resulting in a robust trajectory, where the heat flux over the flight time is less sensitive against perturbations in air density. For this purpose, sensitivities describing the rate of change of the heat flux with respect to perturbations in air density are minimized. Solving the associated optimal control problem is based on direct solution methods, where the problem is discretized and solved as a finite dimensional optimization problem. The robustness is achieved by a two-step optimization. In the first optimization, the nominal problem, where the maximum heat flux is minimized, is to be solved. In the second optimization, high sensitivities are penalized by formulating a new cost function consisting of the sum of the maximum heat flux and weighted sensitivities resulting in robust optimal controls.