%0 Journal Article
%T Two-Aircraft optimal control problem. The in-flight noise reduction*, **
%A Nahayo Fulgence
%A Haddou Mounir
%A Khardi Salah
%A Hamadiche Mahmoud
%J ESAIM : Proceedings
%D 2012
%I EDP Sciences
%R 10.1051/proc/201235026
%X The aim of this paper is to present and solve a mathematical model of a two-aircraft optimal control problem reducing the noise on the ground during the approach. The mathematical modelization of this problem is a non-convex optimal control governed by ordinary non-linear differential equations. To solve this problem, A direct method and a Runge-Kutta RK4 discretization schema are used. This discretization schema is chosed because it is a sufficiently high order and it does-not require computation of the partial derivatives of the aircraft dynamic. The Nonlinear Interior point Trust Region Optimization solver KNITRO is applied. A large set of numerical experiments is presented. The obtained results give feasible trajectories with a significant noise reduction.
%U http://dx.doi.org/10.1051/proc/201235026