Two-Aircraft Dynamic System on Approach. Flight Path and noise Optimization

The aim of this paper is to present and to solve a mathematical model of two-aircraft optimal control problem reducing noise during the approach. This is a non-convex optimal control problem governed by ordinary non-linear differential equations. A Symplectic Partitioned Runge-Kutta discretization and the Pontryaguin maximum principle are used. Discretization scheme provides a sufficiently high order requiring a computation of the partial derivatives of the aircraft dynamic parameters. The nonlinear interior point trust region optimization solver is applied. Numerical experiments and results are presented. They confirm the feasible optimized trajectories contributing to a signicant noise reduction. Symplectic Partitioned - Runge-Kutta algorithm - optimal control problem - AMPL programming - KNITRO - aircraft noise.