R. A. Adams, Sobolev spaces, 1975.

A. A. Agrachev and Y. L. Sachkov, Control theory from the geometric viewpoint
DOI : 10.1007/978-3-662-06404-7

M. S. Aronna, J. F. Bonnans, A. V. Dmitruk, and P. A. Lotito, Quadratic conditions for bang-singular extremals. Numerical Algebra, Control and Optimization, AIMS, special issue in honor of Helmut Maurer, pp.511-546, 2012.
DOI : 10.3934/naco.2012.2.511
URL : https://hal.archives-ouvertes.fr/inria-00605128

M. S. Aronna, J. F. Bonnans, and P. Martinon, A shooting algorithm for problems with singular arcs, INRIA Research Rapport Nr, vol.7763, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00631332

D. M. Azimov, Active sections of rocket trajectories. A survey of research, Avtomat. i Telemekh, issue.11, pp.14-34, 2005.

D. J. Bell and D. H. Jacobson, Singular Optimal Control Problems, 1975.

D. S. Bernstein and V. Zeidan, The singular linear-quadratic regulator problem and the Goh-Riccati equation, 29th IEEE Conference on Decision and Control, pp.334-339, 1990.
DOI : 10.1109/CDC.1990.203608

F. Bonnans, J. Laurent-varin, P. Martinon, and E. Trélat, Numerical study of optimal trajectories with singular arcs for an Ariane 5 launcher, Journal of Guidance, Control, and Dynamics, vol.32, issue.1, pp.51-55, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00312012

B. Bonnard and J. Caillau, 1 Introduction to Nonlinear Optimal Control, Lecture Notes in Control and Inform. Sci, vol.328, pp.1-60, 2006.
DOI : 10.1007/11583592_1

H. J. Bortolossi, M. V. Pereira, and C. Tomei, Optimal hydrothermal scheduling with variable production coefficient, Mathematical Methods of Operations Research (ZOR), vol.55, issue.1, pp.11-36, 2002.
DOI : 10.1007/s001860200174
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.9710

H. Brézis, Analyse fonctionnelle, 1983.

A. E. Bryson, J. , and Y. C. Ho, Applied Optimal Control: Optimization, Estimation, and Control, IEEE Transactions on Systems, Man, and Cybernetics, vol.9, issue.6, 1975.
DOI : 10.1109/TSMC.1979.4310229

R. Bulirsch, Die Mehrzielmethode zur numerischen Losung von nichtlinearen Randwertproblemen und Aufgaben der optimalen Steuerung, 1971.

D. I. Cho, P. L. Abad, and M. Parlar, Optimal production and maintenance decisions when a system experience age-dependent deterioration, Optimal Control Applications and Methods, vol.8, issue.3, pp.153-167, 1993.
DOI : 10.1002/oca.4660140302

A. V. Dmitruk, Quadratic conditions for a weak minimum for singular regimes in optimal control problems, Soviet Math. Doklady, vol.18, issue.2, 1977.

A. V. Dmitruk, Jacobi-type conditions for the problem of Bolza with inequalities, Mathematical Notes of the Academy of Sciences of the USSR, vol.5, issue.No. 3, pp.427-435, 1984.
DOI : 10.1007/BF01139945

A. V. Dmitruk, Jacobi type conditions for singular extremals, Control & Cybernetics, vol.37, issue.2, pp.285-306, 2008.

A. V. Dmitruk, Quadratic Order Optimality Conditions for Extremals Completely Singular in Part of Controls, Selected Papers of the Annual International Conference of the German Operations Research Society, pp.341-346, 2010.
DOI : 10.1007/978-3-642-20009-0_54

A. V. Dmitruk and K. K. Shishov, Analysis of a quadratic functional with a partly singular Legendre condition, Moscow University Comput. Math. and Cybernetics, vol.34, issue.1, pp.16-25, 2010.

A. Ya, A. A. Dubovitskii, and . Milyutin, Extremum problems with constraints, USSR Comp. Math. and Math. Phys, vol.5, issue.3, pp.1-80, 1965.

R. Fletcher, Practical methods of optimization, 1980.
DOI : 10.1002/9781118723203

R. H. Goddard, A Method of Reaching Extreme Altitudes, Smithsonian Miscellaneous Collections. Smithsonian institution, vol.71, issue.2, 1919.

B. S. Goh, Necessary Conditions for Singular Extremals Involving Multiple Control Variables, SIAM Journal on Control, vol.4, issue.4, pp.716-731, 1966.
DOI : 10.1137/0304052

B. S. Goh, Necessary Conditions for the Singular Extremals in the Calculus of Variations, 1966.

B. S. Goh, The Second Variation for the Singular Bolza Problem, SIAM Journal on Control, vol.4, issue.2, pp.309-325, 1966.
DOI : 10.1137/0304026

B. S. Goh, Optimal singular control for multi-input linear systems, Journal of Mathematical Analysis and Applications, vol.20, issue.3, pp.534-539, 1967.
DOI : 10.1016/0022-247X(67)90079-0

B. S. Goh, Compact forms of the generalized legendre-clebsch conditions and the computation of singular control trajectories, Proceedings of the American Control Conference, pp.3410-3413, 1995.

B. S. Goh, Optimal singular rocket and aircraft trajectories, 2008 Chinese Control and Decision Conference, pp.1531-1536, 2008.
DOI : 10.1109/CCDC.2008.4597574

M. R. Hestenes, Applications of the theory of quadratic forms in Hilbert space to the calculus of variations, Pacific Journal of Mathematics, vol.1, issue.4, pp.525-581, 1951.
DOI : 10.2140/pjm.1951.1.525

D. G. Hull, Optimal Guidance for Quasi-planar Lunar Ascent, Journal of Optimization Theory and Applications, vol.135, issue.2, pp.353-372, 2011.
DOI : 10.1007/s10957-011-9884-5

H. J. Kelley, A second variation test for singular extremals, AIAA Journal, vol.2, issue.8, pp.1380-1382, 1964.
DOI : 10.2514/3.2562

H. J. Kelley, R. E. Kopp, and H. G. Moyer, 3 Singular Extremals, Topics in Optimization, pp.63-101, 1967.
DOI : 10.1016/S0076-5392(09)60039-4

P. Kunkel and V. Mehrmann, Differential-algebraic equations: Analysis and numerical solution, EMS Textbooks in Mathematics. European Mathematical Society (EMS), 2006.
DOI : 10.4171/017

S. Kurcyusz and J. Zowe, Regularity and stability for the mathematical programming problem in Banach spaces, Applied Mathematics and Optimization, pp.49-62, 1979.

D. F. Lawden, Optimal trajectories for space navigation, Butterworths, 1963.

H. Maurer, Numerical solution of singular control problems using multiple shooting techniques, Journal of Optimization Theory and Applications, vol.8, issue.2, pp.235-257, 1976.
DOI : 10.1007/BF00935706

H. Maurer and W. Gillessen, Anwendungen der Mehrzielmethode auf die numerische L??sung von Steuerungsproblemen mit beschr??nkten Zustandsvariablen, Computing, vol.22, issue.No. 3, pp.105-126, 1975.
DOI : 10.1007/BF02252860

H. Maurer, J. Kim, and G. Vossen, On A State-Constrained Control Problem in Optimal Production and Maintenance, Optimal Control and Dynamic Games of Advances in Computational Management Science, pp.289-308, 2005.
DOI : 10.1007/0-387-25805-1_17

H. Maurer and N. P. Osmolovskii, Second order sufficient optimality conditions for a control problem with continuous and bang-bang control components: Riccati approach, System modeling and optimization, pp.411-429, 2009.

A. A. Milyutin, On quadratic conditions for an extremum in smooth problems with a finite-dimensional range. Methods of the Theory of Extremal Problems in Economics, pp.138-177, 1981.

A. A. Milyutin and N. P. Osmolovskii, Calculus of variations and optimal control, 1998.

H. J. Oberle, Numerische Behandlung singulärer Steuerungen mit der Mehrzielmethode am Beispiel der Klimatisierung von Sonnenhäusern, 1977.

H. J. Oberle, On the numerical computation of minimum-fuel, Earth-Mars transfer, Journal of Optimization Theory and Applications, vol.22, issue.3, pp.447-453, 1977.
DOI : 10.1007/BF00932866

H. J. Oberle, Numerical computation of singular control problems with application to optimal heating and cooling by solar energy, Applied Mathematics & Optimization, vol.5, issue.1, pp.297-314, 1979.
DOI : 10.1007/BF01442560

H. J. Oberle, Numerical computation of singular control functions in trajectory optimization problems, Journal of Guidance, Control, and Dynamics, vol.13, issue.1, pp.153-159, 1990.
DOI : 10.2514/3.20529

H. J. Oberle and K. Taubert, Existence and Multiple Solutions of the Minimum-Fuel Orbit Transfer Problem, Journal of Optimization Theory and Applications, vol.6, issue.2, pp.243-262, 1997.
DOI : 10.1023/A:1022627003404

N. P. Osmolovskii, Theory of higher order conditions in optimal control, 1988.

H. J. Pesch, A practical guide to the solution of real-life optimal control problems, Control Cybernet, vol.23, issue.12, pp.7-60, 1994.

L. Pontryagin, V. Boltyanski, R. Gamkrelidze, and E. Michtchenko, The Mathematical Theory of Optimal Processes, 1962.

H. M. Robbins, A Generalized Legendre-Clebsch Condition for the Singular Cases of Optimal Control, IBM Journal of Research and Development, vol.11, issue.4, pp.361-372, 1967.
DOI : 10.1147/rd.114.0361

E. Trélat, Optimal Control and Applications to Aerospace: Some Results and Challenges, Journal of Optimization Theory and Applications, vol.21, issue.1, pp.713-758, 2012.
DOI : 10.1007/s10957-012-0050-5