Two-aircraft optimal control problem. The in-flight noise reduction. (English) Zbl 1357.49013
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 |