Nahayo, Fulgence; Haddou, Mounir; Khardi, Salah; Hamadiche, Mahmoud; Ndimubandi, Jean Two-aircraft optimal control problem. The in-flight noise reduction. (English) Zbl 1357.49013 ESAIM, Proc. 35, 269-274 (2012). Summary: 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. MSC: 49J15 Existence theories for optimal control problems involving ordinary differential equations 49M20 Numerical methods of relaxation type 49N90 Applications of optimal control and differential games 93C10 Nonlinear systems in control theory Software:KNITRO; AMPL PDFBibTeX XMLCite \textit{F. Nahayo} et al., ESAIM, Proc. 35, 269--274 (2012; Zbl 1357.49013) Full Text: DOI