Robust noise optimal approach trajectories

A methodology is presented to calculate optimal flight tracks in the presence of uncertainties. To this end, a bi-level optimal control formulation is used consisting of an upper level parameter optimization problem and multiple embedded lower level optimal control problems. The upper level problem determines the horizontal flight track that minimizes statistical information such as mean or variance of the lower level cost functions. The lower level problems are tasked with minimizing a given cost function such as flight time, number of awakenings or a combination thereof while following the specified track. Stochastic collocation is used to efficiently determine the solution statistics. A numerical example is given where a robust optimal approach trajectory on Salzburg Airport, Austria, is determined for uniformly distributed wind speed.