Évitement de conflits aériens par une régulation subliminale en vitesse : modélisation & résolution via le contrôle optimal

Loïc Cellier 1
1 MAIA-OPTIM - ENAC Equipe MAIAA-OPTIM
MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien
Abstract : The purpose of this doctoral thesis is to study models and solution techniques based on optimal control approaches to address air traffic management problems. Motivated by the growth of air traffic volume, and by the advances in optimal control theory, this research works focus on analysing aircraft conflict avoidance problem. This study allows development of new approaches and algorithms to help air traffic controllers. In the framework of air traffic management, to ensure the minimum safety distances between aircraft, in tactical phases and en-route flight configurations, this thesis focusses on a subliminal velocity regulation strategy to perform the separation, while preserving the aircraft predefined trajectories. A numerical optimal control solution approach as the direct shooting method, wherein involves a total or partial discretization of the problem, transforms the initial problem into a large scale nonlinear programming problem. This kind of methods could generate large-size optimization problems which are numerically difficult to solve. Depending on the number of variables which involved, this approaches could be too expensive in terms of computation time. Moreover, the state-variables constraints of the problem lead to numerical difficulties, e.g., considering the indirect numerical shooting method. Tailored on aircraft conflict avoidance problems, a detection and a determination of a priori conflict zones allow the decomposition of the optimal control problem into sub-problems, easier to solve than the original one. Solving the off -zone sub-problems can be addressed using the Pontryagin maximum principle, which allows in this case directly the solution. A combination of direct numerical shooting method and application of conditions of Pontryagin’s maximum principle is proposed, and numerical experiments validate this approach.
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Loïc Cellier. Évitement de conflits aériens par une régulation subliminale en vitesse : modélisation & résolution via le contrôle optimal. Optimisation et contrôle [math.OC]. UPS Toulouse - Université Toulouse 3 Paul Sabatier, 2015. Français. ⟨tel-02139581⟩

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