Authors: F. Nahayo ^1,2; S. Khardi ²; J. Ndimubandi ¹; M. Haddou ; M. Hamadiche ³

• 1 Mathematics Department, Faculty of Science, University of Burundi
• 2 Laboratoire Transport et Environnement
• 3 Laboratoire de Mecanique des Fluides et d'Acoustique

This contribution aims to develop an acoustic optimization model of flight paths minimizing two-aircraft perceived noise on the ground. It is about minimizing the noise taking into account all the constraints of flight without conflict. The flight dynamics associated with a cost function generate a non-linear optimal control problem governed by ordinary non-linear differential equations. To solve this problem, the theory of necessary conditions for optimal control problems with instantaneous constraints is well used. This characterizes the optimal solution as a local one when the newtonian approach has been used alongside the optimality conditions of Karush-Kuhn-Tucker and the trust region sequential quadratic programming. The SQP methods are suggested as an option by commercial KNITRO solver under AMPL programming language. Among several possible solution, it was shown that there is an optimal trajectory (for each aircraft) leading to a reduction of noise levels on the ground.