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In the paper at hand, the simultaneous computation of fuel-minimal approach trajectories for multiple aircraft present in the vicinity of an airport at a certain point in time is treated. The trajectory optimization task includes the determination of the optimal aircraft queuing sequence on the ILS glide path, minimizing the total fuel consumption of all aircraft involved. The trajectory optimization is based on aircraft point-mass simulation models with the aircraft characteristics taken from the BADA database of EUROCONTROL. Specifically tailored path constraints are introduced that define the permitted airspace and that enforce the aircraft to follow the ILS glide path once they have passed the final approach fix. Furthermore, path constraints are implemented that guarantee certain separation distances between the involved aircraft throughout the approach flights. An algorithmic procedure is set up which is aimed at producing a good initial guess for the multi-aircraft trajectory optimization task. The proposed framework is applied to a generic scenario where a fuel-efficient approach scheduling for four civil passenger aircraft has to be determined.
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.