This paper addresses the analysis of aircraft control capabilities during the cruise
phase (flying at the established level with practically constant configuration and speed) in
the presence of windshears. The study uses a point-mass aircraft model describing flight in a
vertical plane. The problem is formulated as a differential game against wind disturbances.
The first player, autopilot, controls the angle of attack and the power setting, whereas the
second player, wind, produces dangerous gusts. The state variables of the model are subjected
to constraints expressing aircraft safety conditions. Namely, the altitude, path inclination, and
velocity are constrained. Viability theory is used to find the so-called viability 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 grid methods developed by the
authors and implemented on a multiprocessor computer system.

• Aircraft Control During Cruise Flight in Windshear Conditions: Viability Approach