Neighboring Optimal Aircraft Guidance in Winds

The technique of neighboring optimal control is extended to handle cases of parameter change in the system dynamic model. This extension is used to develop an algorithm for optimizing horizontal aircraft trajectories in general wind fields using time-varying linear feedback gains. The minimum-time problem for an airplane traveling horizontally between two points in a variable wind field (a type of Zermelo problem) is used to illustrate how perturbations in system parameters can be accounted for by augmenting the dynamic model with additional bias states. For the special case of a constant wind shear in the cross-track direction, analytical and numerical results are derived for bias perturbations. Numerical simulations are presented to demonstrate the performance of the proposed state-augmentation technique. An additional example is used to demonstrate an algorithm to compute near-optimal trajectories in general wind fields. The algorithm is based on nondimensionalizing the neighboring optimal control solutions and using piecewise linearly varying wind and horizontal wind shear parameters. One proposed application of this technique is to the computation and real-time update of time-optimal trajectories in wind fields by onboard flight management systems and by ground-based air traffic management automation tools.