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Fonctions de navigation stochastiques : application à la planification robuste de trajectoires d'avions

Abstract : Context: As air traffic continues to increase, new aircraft trajectory plannification methods need to be implemented. Navigation functions have been implemented to this end, but their reliability in an uncertain environment is yet to be demonstrated. Aims: Implementing new tools based on the Hadamard variational formula to take into account the uncertainties on the longitudinal position of aircraft when computing the navigation function. Methods: The Hadamard variation makes it possible to assess the effect of a domain boundary variation on the trajectories computed using harmonic navigation functions. Using this variational formula requires the developpment of an efficient method to numerically compute the Green's function. Results: We demonstrate in this thesis that it is possible to numerically determine the Green's function and its derivatives with a semi-analytical method. Furthermore, the Green's function determined in this manner can be used to compute the Hadamard variational formula. Conclusions: This semi-analytical Green's function can be used to compute the Hadamard variational formula and makes it possible to account for uncertainties on the position of obstacles. We also give some leads on how to improve this method based on the Hadamard variational formula, most notably on how to reduce computation time and improve accuracy.
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https://hal-enac.archives-ouvertes.fr/tel-02089324
Contributor : Isabelle Santos <>
Submitted on : Wednesday, April 3, 2019 - 4:12:09 PM
Last modification on : Tuesday, October 20, 2020 - 10:32:07 AM

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Isabelle Santos. Fonctions de navigation stochastiques : application à la planification robuste de trajectoires d'avions. Analyse numérique [math.NA]. Université Toulouse 3 Paul Sabatier, 2019. Français. ⟨tel-02089324⟩

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