Geodesic
Two-Aircraft optimal control problem. The in-flight noise reduction,
Fulgence Nahayo1 ; Mounir Haddou2 ; Salah Khardi3 ; Mahmoud Hamadiche4 ; Jean Ndimubandi5
1 Infomaths, University Claude Bernard of Lyon 1 France - LTE-IFSTTAR - University of Burundi,E-Mail: nahayo
2 INSA-IRMAR, UMR-CNRS 6625, Rennes - France
3 LTE, The French Institute of Science and Technology for Transport, Development and Networks, Lyon - France
4 LMFA,University Claude Bernard of Lyon 1, France
5 Mathematics departement, University of Burundi, Bujumbura - Burundi
ESAIM. Proceedings, Tome 35 (2012), pp. 269-274.

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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.
DOI : 10.1051/proc/201235026

Fulgence Nahayo 1 ; Mounir Haddou 2 ; Salah Khardi 3 ; Mahmoud Hamadiche 4 ; Jean Ndimubandi 5

1 Infomaths, University Claude Bernard of Lyon 1 France - LTE-IFSTTAR - University of Burundi,E-Mail: nahayo
2 INSA-IRMAR, UMR-CNRS 6625, Rennes - France
3 LTE, The French Institute of Science and Technology for Transport, Development and Networks, Lyon - France
4 LMFA,University Claude Bernard of Lyon 1, France
5 Mathematics departement, University of Burundi, Bujumbura - Burundi 
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     author = {Fulgence Nahayo and Mounir Haddou and Salah Khardi and Mahmoud Hamadiche and Jean Ndimubandi},
     title = {Two-Aircraft optimal control problem. {The} in-flight noise reduction,},
     journal = {ESAIM. Proceedings},
     pages = {269--274},
     publisher = {mathdoc},
     volume = {35},
     year = {2012},
     doi = {10.1051/proc/201235026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201235026/}
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Fulgence Nahayo; Mounir Haddou; Salah Khardi; Mahmoud Hamadiche; Jean Ndimubandi. Two-Aircraft optimal control problem. The in-flight noise reduction,. ESAIM. Proceedings, Tome 35 (2012), pp. 269-274. doi : 10.1051/proc/201235026. http://geodesic.mathdoc.fr/articles/10.1051/proc/201235026/

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