Aircraft robust trajectory optimization using nonintrusive polynomial chaos

The development of algorithms for aircraft robust dynamic optimization considering uncertainties (for example, trajectory optimization) is relatively limited compared to aircraft robust static optimization (for example, configuration shape optimization). In this paper, an approach for dynamic optimization considering uncertainties is developed and applied to robust aircraft trajectory optimization. In the present approach, the nonintrusive polynomial chaos expansion scheme is employed to convert a robust trajectory optimization problem with stochastic ordinary differential equations into an equivalent deterministic trajectory optimization problem with deterministic ordinary differential equations. Two computational strategies for trajectory optimization considering uncertainties are compared. The performance of the developed method is studied by considering a classical deterministic trajectory optimization problem of supersonic aircraft short-time climb with uncertainties in the aerodynamic data. Detailed numerical studies are presented to illustrate the computational features of the proposed approach.