A. Vink, Eatchip medium term conflict detection: Part 1 eatchip context, Proceeding of the Air Traffic Management Seminar, 1997.

E. Atkins, I. Portillo, and M. J. Strube, Emergency Flight Planning Applied to Total Loss of Thrust, Journal of Aircraft, vol.43, issue.4, pp.1205-1216, 2006.
DOI : 10.2514/1.18816

E. Bakolas, Y. Zhao, and P. Tsiotras, Initial guess generation for aircraft landing trajectory optimization, AIAA Guidance, Navigation, and Control Conference, 2011.

R. Bartels, J. Beatty, and B. A. Barskyn, An introduction to splines for use in computer graphics and geometric modeling, Computer graphics, 1998.

B. D. Mcnally, R. E. Bach, and C. W. , Field test evaluation of the CTAS conflict prediction and trial planning capability, Guidance, Navigation, and Control Conference and Exhibit, 1998.
DOI : 10.2514/6.1998-4480

V. M. Becerra, Psopt optimal control solver user manual, 2011.

J. Bellingham, Y. Kuwata, and J. How, Stable Receding Horizon Trajectory Control for Complex Environments, AIAA Guidance, Navigation, and Control Conference and Exhibit, 2003.
DOI : 10.2514/6.2003-5635

J. T. Betts, Survey of Numerical Methods for Trajectory Optimization, Journal of Guidance, Control, and Dynamics, vol.21, issue.2, pp.193-207, 1998.
DOI : 10.2514/2.4231

J. T. Betts, N. Biehn, S. L. Campbell, and W. P. Huffman, Compensating for order variation in mesh refinement for direct transcription methods, Journal of Computational and Applied Mathematics, vol.125, issue.1-2, pp.147-158, 2000.
DOI : 10.1016/S0377-0427(00)00465-9

J. T. Betts and W. Huffman, Sparse optimal control software SOCS Mathematics and Engineering Analysis Technical Document MEALR-085, 1997.

J. Betts and W. P. Huffman, Mesh refinement in direct transcription methods for optimal control, Optimal Control Applications and Methods, vol.10, issue.1, pp.1-21, 1998.
DOI : 10.1002/(SICI)1099-1514(199801/02)19:1<1::AID-OCA616>3.0.CO;2-Q

T. Binder, L. Blank, W. Dahmen, and W. Marquardt, Grid refinement in multiscale dynamic optimization, 2000.
DOI : 10.1016/S1570-7946(00)80007-3

C. Birkhoff and . De-boor, Piecewise polynomial interpolation and approximation, Proceeding of the General Motors Symposium of 1964, General Motors, 1964.

R. Bulirsch, F. Montrone, and H. J. Pesch, Abort landing in the presence of windshear as a minimax optimal control problem, part 1: Necessary conditions, Journal of Optimization Theory and Applications, vol.15, issue.1, pp.1-23, 1991.
DOI : 10.1007/BF00940502

J. W. Burrows, Fuel-optimal aircraft trajectories with fixed arrival times, Journal of Guidance, Control, and Dynamics, vol.6, issue.1, pp.14-19, 1983.
DOI : 10.2514/3.19796

C. Meckiff, R. Chone, and N. J. , The tactical load smoother for multi-sector planning, Proceeding of the Air Traffic Management Seminar, 1998.

S. Chaimatanan, D. Delahaye, and M. Mongeau, Conflict free strategic planning, Proceeding of the 2012 Interdisciplinary Science for Innovative Air Traffic Management conference, p.2012

A. Chakravarty, Four-dimensional fuel-optimal guidance in the presence of winds, Journal of Guidance, Control, and Dynamics, vol.8, issue.1, pp.16-22, 1985.
DOI : 10.2514/3.19929

L. Davis, Handbook of genetic algorithms, 1991.

C. De-boor, A practical guide to splines, 1978.
DOI : 10.1007/978-1-4612-6333-3

D. J. Brudnicki and A. L. Mcfarland, User request evaluation tool (uret) conflict probe performance and benefits assessment, Proceeding of the Air Traffic Management Seminar, 1997.

N. Dougui, D. Delahaye, M. Puechmorel, and . Mongeau, A light-propagation model for aircraft trajectory planning, Journal of Global Optimization, vol.7, issue.2, 2012.
DOI : 10.1007/s10898-012-9896-1
URL : https://hal.archives-ouvertes.fr/hal-00935210

P. J. Enright and B. A. Conway, Discrete approximations to optimal trajectories using direct transcription and nonlinear programming, Journal of Guidance, Control, and Dynamics, vol.15, issue.4, pp.994-1002, 1992.
DOI : 10.2514/3.20934

J. Evans, Reducing severe weather delays in congested airspace with weather support for tactical air traffic management, Proceeding of the Air Traffic Management Seminar, 2003.

D. B. Kirk, Problem analysis resolution and ranking (parr) development and assessment, Proceeding of the Air Traffic Management Seminar, 2001.

A. Masalonis, Using Probabilistic Demand Predictions for Traffic Flow Management Decision Support, AIAA Guidance, Navigation, and Control Conference and Exhibit, 2004.
DOI : 10.2514/6.2004-5231

V. Sud, Air traffic flow management collaborative routing coordination tools, 2001.

H. N. Swensen, Design and operational evaluation of the traffic management advisor at the forth worth air route traffic control center, Proceeding of the Air Traffic Management Seminar, 1997.

G. M. Ewing, Calculus of variations with applications, 1969.

G. Farin and H. Dianne, The essentials of cagd, 2000.

G. Farin, Curves and surfaces for computer aided geometric design. a practical guide, 1993.

C. Douglas and . Giancoli, Physics for scientists and engineers with modern physics, 1989.

Q. Gong, F. Fahroo, and I. M. Ross, Spectral Algorithm for Pseudospectral Methods in Optimal Control, Journal of Guidance, Control, and Dynamics, vol.31, issue.3, pp.460-471, 2008.
DOI : 10.2514/1.32908

W. Grimm, K. Well, and H. Oberle, Periodic control for minimum-fuel aircraft trajectories, Journal of Guidance, Control, and Dynamics, vol.9, issue.2, pp.169-174, 1986.
DOI : 10.2514/3.20086

H. Erzberger, R. A. Paielli, D. R. Isaacson, and M. M. , Conflict detection in the presence of prediction error, Proceeding of the Air Traffic Management Seminar, 1997.

C. R. Hargraves and S. W. Paris, Direct trajectory optimization using nonlinear programming and collocation, Journal of Guidance, Control, and Dynamics, vol.15, pp.994-1002, 1992.

T. Hearth and M. , Scientific computing, an introductory survey, Computer graphics, 2002.

M. R. Jackson, Y. Zhao, and R. A. Slattery, Sensitivity of Trajectory Prediction in Air Traffic Management, Journal of Guidance, Control, and Dynamics, vol.22, issue.2, pp.219-228, 1999.
DOI : 10.2514/2.4398

M. Jacobson and U. T. Ringertz, Airspace Constraints in Aircraft Emission Trajectory Optimization, Journal of Aircraft, vol.47, issue.4, pp.1256-1265, 2010.
DOI : 10.2514/1.47109

S. Jain and P. Tsiotras, Multiresolution-based direct trajectory optimization, 2007 46th IEEE Conference on Decision and Control, pp.1424-1436, 2008.
DOI : 10.1109/CDC.2007.4434076

S. Jain and P. Tsiotras, Trajectory Optimization Using Multiresolution Techniques, Journal of Guidance, Control, and Dynamics, vol.31, issue.5, pp.1424-1436, 2008.
DOI : 10.2514/1.32220

M. R. Jardin and A. E. Bryson, Neighboring Optimal Aircraft Guidance in Winds, Journal of Guidance, Control, and Dynamics, vol.24, issue.4, pp.710-715, 2001.
DOI : 10.2514/2.4798

S. Lavalle, Planning algorithms, 2006.
DOI : 10.1017/CBO9780511546877

W. Liu and I. Hwang, Probabilistic aircraft mid-air conflict resolution using stochastic optimal control, IEEE Intelligent Transportation Systems Transactions and Magazine, 2012.

P. Lu, Regulation About Time-Varying Trajectories: Precision Entry Guidance Illustrated, Journal of Guidance, Control, and Dynamics, vol.22, issue.6, pp.784-790, 1999.
DOI : 10.2514/2.4479

M. Berger and B. Gostiaux, Differential geometry: Manifolds, curves and surfaces, 1988.
DOI : 10.1007/978-1-4612-1033-7

A. Miele, Optimal trajectories and guidance trajectories for aircraft flight through windshears, 29th IEEE Conference on Decision and Control, 1990.
DOI : 10.1109/CDC.1990.203686

S. Mondoloni, S. M. Pagli, and S. Green, Trajectory modeling accuracy for air traffic management decision support tools, Proceeding of the ICAS Conference, 2002.

H. J. Oberle and W. Grimm, BNDSCO -A program for the numerical solution of optimal control problems, 1989.

T. Ohtsuka, Quasi-Newton-Type Continuation Method for Nonlinear Receding Horizon Control, Journal of Guidance, Control, and Dynamics, vol.25, issue.4, pp.685-692, 2002.
DOI : 10.2514/2.4935

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

L. S. Pontryagin, V. G. Boltyanski, R. V. Gamkrelidze, and E. F. Mischenko, The mathematical theory of optimal processes, 1962.

C. Ptrs, Y. Pailhas, P. Patron, Y. Petillot, J. Evans et al., Path Planning for Autonomous Underwater Vehicles, Path planning for autonomous underwater vehicles, pp.331-341, 2007.
DOI : 10.1109/TRO.2007.895057

R. Coppenbarger, R. Lanier, D. Sweet, and D. S. , Design and development of the enroute descent advisor (eda) for conflict-free arrival metering, 2004.

R. Slattery and Y. Zhao, Trajectory Synthesis for Air Traffic Automation, Journal of Guidance, Control, and Dynamics, vol.20, issue.2, pp.232-238, 1997.
DOI : 10.2514/2.4056

J. O. Ramsay and B. W. Silverman, Functional data analysis, 2005.

A. Rao, G. T. Benson, and . Huntington, User's manual for GPOPS version 4.x: A matlab package for software for solving multiple-phase optimal control problems using hp-adaptive pseudospectral methods, 2011.

E. Roche, Parsing with finite-state transducers, Finite-State Language Processing, 1997.

I. M. Ross, user's manual for DIDO: A MATLAB application package for solving optimal control problems, 2005.

R. D. Russell and L. Shampine, A collocation method for boundary value problems, Numerische Mathematik, vol.6, issue.1, pp.13-36, 1972.
DOI : 10.1007/BF01395926

H. F. Ryan, M. Paglione, and S. Green, Review of trajectory accuracy methodology and comparison of error measure metrics, 2004.

S. Mondoloni and I. Bayraktuta, Impact of factors, conditions and metrics on trajectory prediction accuracy, Proceeding of the Air Traffic Management Seminar, 2005.

S. Swierstra and S. Green, Common trajectory prediction capability for decision support tools, Proceeding of the Air Traffic Management Seminar, 2003.

T. Schouwenaars, J. How, and E. Feron, Receding horizon path planning with implicit safety guarantees, American Control Conference, pp.5576-5581, 2004.

T. Schouwenaars, M. Valenti, E. Feron, J. How, and E. Roche, Linear Programming and Language Processing for Human-Unmanned Aerial-Vehicle Team Missions, Journal of Guidance, Control, and Dynamics, vol.29, issue.2, pp.303-313, 2006.
DOI : 10.2514/1.13162

R. L. Schultz, Three-dimensional trajectory optimization for aircraft, Journal of Guidance, Control, and Dynamics, vol.13, issue.6, pp.936-943, 1990.
DOI : 10.2514/3.20564

A. Schwartz, Theory and implementation of numerical methods based on runge-kutta integration for solving optimal control problems, 1996.

J. A. Sethian, Fast marching methods, SIAM review, pp.41-199, 1999.

J. A. Sethian and A. Vladimirsky, Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms, SIAM Journal on Numerical Analysis, vol.41, issue.1, pp.325-363, 2003.
DOI : 10.1137/S0036142901392742

H. Seywald, Long flight-time range-optimal aircraft trajectories, Journal of Guidance, Control, and Dynamics, vol.19, issue.1, pp.242-244, 1994.
DOI : 10.2514/3.21605

H. Seywald and E. M. Cliff, Neighboring optimal control based feedback law for the advanced launch system, Journal of Guidance, Control, and Dynamics, vol.17, issue.6, pp.1154-1162, 1994.
DOI : 10.2514/3.21327

H. Seywald, E. M. Cliff, and K. Well, Range optimal trajectories for an aircraft flying in the vertical plane, Journal of Guidance, Control, and Dynamics, vol.17, issue.2, pp.389-398, 1994.
DOI : 10.2514/3.21210

R. A. Slattery and Y. Zhao, Trajectory Synthesis for Air Traffic Automation, Journal of Guidance, Control, and Dynamics, vol.20, issue.2, pp.232-238, 1997.
DOI : 10.2514/2.4056

B. Sridhar, N. Y. Ng, H. K. , and C. , Aircraft Trajectory Optimization and Contrails Avoidance in the Presence of Winds, Journal of Guidance, Control, and Dynamics, vol.34, issue.5, pp.1577-1583, 2011.
DOI : 10.2514/1.53378

M. J. Strube, R. M. Sanner, and E. Atkins, Dynamic Flight Guidance Recalibration After Actuator Failure, AIAA 1st Intelligent Systems Technical Conference, 2004.
DOI : 10.2514/6.2004-6255

C. Tomlin, G. J. Pappas, and S. Sastry, Conflict resolution for air traffic management: A study in multi-agent hybrid systems, IEEE Trans. on Automatic Control, vol.43, 1998.

R. Weiss, The Application of Implicit Runge-Kutta and Collocation Methods to Boundary-Value Problems, Mathematics of Computation, vol.28, issue.126, pp.449-464, 1974.
DOI : 10.2307/2005918

P. Williams, Application of Pseudospectral Methods for Receding Horizon Control, Journal of Guidance, Control, and Dynamics, vol.27, issue.2, pp.310-314, 2004.
DOI : 10.2514/1.5118

H. Yan, I. M. Fahroo, and . Ross, Real-Time Computation of Neighboring Optimal Control Laws, AIAA Guidance, Navigation, and Control Conference and Exhibit, 2002.
DOI : 10.2514/6.2002-4657

Y. Zhao, Efficient and robust aircraft landing trajectory optimization, 2011.

Y. Zhao and P. Tsiotras, Density Functions for Mesh Refinement in Numerical Optimal Control, Stable receding horizon trajectory control for complex environment, pp.271-277, 2010.
DOI : 10.2514/1.45852