https://hal-enac.archives-ouvertes.fr/hal-00913243Delahaye, DanielDanielDelahayeMAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien - ENAC - Ecole Nationale de l'Aviation CivilePuechmorel, StéphaneStéphanePuechmorelENAC - Ecole Nationale de l'Aviation CivileTsiotras, PanagiotisPanagiotisTsiotrasGA TECH - Daniel Guggenheim School of Aerospace Engineering - Georgia Institute of Technology [Atlanta]Féron, EricEricFéronGA TECH - Daniel Guggenheim School of Aerospace Engineering - Georgia Institute of Technology [Atlanta]Mathematical Models for Aircraft Trajectory Design : A SurveyHAL CCSD2014[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Smith, Céline2014-01-10 15:25:082021-10-19 11:02:492014-01-13 13:00:47enConference papershttps://hal-enac.archives-ouvertes.fr/hal-00913243/document10.1007/978-4-431-54475-3_12application/pdf1Air traffic management ensures the safety of flight by optimizing flows and maintaining separation between aircraft. After giving some definitions, some typical feature of aircraft trajectories are presented. Trajectories are objects belonging to spaces with infinite dimensions. The naive way to address such problem is to sample trajectories at some regular points and to create a big vector of positions (and or speeds). In order to manipulate such objects with algorithms, one must reduce the dimension of the search space by using more efficient representations. Some dimension reduction tricks are then presented for which advantages and drawbacks are presented. Then, front propagation approaches are introduced with a focus on Fast Marching Algorithms and Ordered upwind algorithms. An example of application of such algorithm to a real instance of air traffic control problem is also given. When aircraft dynamics have to be included in the model, optimal control approaches are really efficient. We present also some application to aircraft trajectory design. Finally, we introduce some path planning techniques via natural language processing and mathematical programming.