Air traffic complexity based on dynamical systems

Daniel Delahaye (1) , Stéphane Puechmorel (1)

1 ENAC - Ecole Nationale de l'Aviation Civile

This paper presents a new air traffic complexity metric based on dynamical systems. Based on a set of radar observations (position and speed) a vector field interpolating these data is constructed. Once the field has been obtained, the Lyapunov spectrum of the associated dynamical system is computed on points evenly spaced on a spatial grid. The results of the computations are summarized on complexity maps, with high values indicating areas to avoid or to carefully monitor. A first approach based on linear dynamical system enable to compute an aggregate complexity metric. In order to produce complexity maps, two extensions of the previous approach have been developed (one in space and another in space and time). Finally, an approximation is proposed in order to localize the computation of the vector field by the mean of Local Linear Models.

Mots clés: Lyapunov spectrum; air traffic complexity metric; complexity maps; linear dynamical system; local linear models; radar observations

Domaines: Optimisation et contrôle [math.OC]

Daniel Delahaye, Stéphane Puechmorel. Air traffic complexity based on dynamical systems. CDC 2010, 49th IEEE Conference on Decision and Control, Dec 2010, Atlanta, United States. pp 2069-2074, ⟨10.1109/CDC.2010.5718004⟩. ⟨hal-00938405⟩