Viability Approach to Aircraft Control in Wind Shear Conditions

This paper addresses the analysis of aircraft control capabilities in the presence of wind shears. The cruise flight phase (flying at the established level with practically constant configuration and speed) is considered. The study utilizes a point-mass aircraft model describing both vertical and lateral motions. As a particular case, a reduced model of lateral motion is derived from the full one. State variables of the models are constrained according to aircraft safety conditions, and differential games where a guiding system, the first player, works against wind disturbances, the second player, are considered. Viability theory is used to find the leadership kernel, the maximal subset of the state constraint where the aircraft trajectories can remain arbitrary long if the first player utilizes an appropriate feedback control, and the second player generates any admissible disturbances. The computations are based on a theoretical background resulting in a grid method developed by the authors. The corresponding software is implemented on a multiprocessor computer system.