B. Bonnard, J. Caillau, and E. Trélat, Second order optimality conditions in the smooth case and applications in optimal control, ESAIM: Control, Optimisation and Calculus of Variations, vol.6, issue.2, pp.207-236, 2007.
DOI : 10.1051/cocv:2001115

URL : https://hal.archives-ouvertes.fr/hal-00086380

B. Bonnard and M. Chyba, Singular trajectories and their role in control theory, 2003.

B. Bonnard, L. Faubourg, G. Launay, and E. Trélat, Optimal control with state constraints and the space shuttle re-entry problem, Journal of Dynamical and Control Systems, vol.9, issue.2, pp.155-199, 2003.
DOI : 10.1023/A:1023289721398

URL : https://hal.archives-ouvertes.fr/hal-00086315

R. F. Brammer, Controllability in Linear Autonomous Systems with Positive Controllers, SIAM Journal on Control, vol.10, issue.2, pp.339-353, 1972.
DOI : 10.1137/0310026

A. Bressan and F. Rampazzo, On differential systems with vector-valued impulsive controls, Boll. Un. Mat. Ital. B, vol.2, issue.73, pp.641-656, 1988.

A. Bressan and F. Rampazzo, Impulsive control systems with commutative vector fields, Journal of Optimization Theory and Applications, vol.78, issue.4, pp.67-83, 1991.
DOI : 10.1007/978-1-4612-6380-7

J. Coron, Control and nonlinearity, 2007.
DOI : 10.1090/surv/136

J. Coron and E. Trélat, Global Steady-State Controllability of One-Dimensional Semilinear Heat Equations, SIAM Journal on Control and Optimization, vol.43, issue.2, pp.549-569, 2004.
DOI : 10.1137/S036301290342471X

J. Coron and E. Trélat, GLOBAL STEADY-STATE STABILIZATION AND CONTROLLABILITY OF 1D SEMILINEAR WAVE EQUATIONS, Communications in Contemporary Mathematics, vol.10, issue.04, pp.535-567, 2006.
DOI : 10.1016/S0294-1449(16)30221-9

URL : https://hal.archives-ouvertes.fr/hal-00086370

N. Forcadel, Z. Rao, and H. Zidani, State-Constrained Optimal Control Problems of Impulsive Differential Equations, Applied Mathematics & Optimization, vol.46, issue.6, pp.1-19, 2013.
DOI : 10.1137/040620734

URL : https://hal.archives-ouvertes.fr/hal-00653671

R. V. Gamkrelidze, Principles of optimal control theory Translated from Russian by, Mathematical Concepts and Methods in Science and Engineering, vol.7, 1978.

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

R. F. Hartl, S. P. Sethi, and R. G. Vickson, A Survey of the Maximum Principles for Optimal Control Problems with State Constraints, SIAM Review, vol.37, issue.2, pp.181-218, 1995.
DOI : 10.1137/1037043

W. P. Heemels and M. K. , Controllability of linear systems with input and state constraints, 2007 46th IEEE Conference on Decision and Control, pp.12-14, 2007.
DOI : 10.1109/CDC.2007.4434588

A. Isidori, Nonlinear control systems, 1995.

V. Jurdjevic, Geometric control theory, volume 52 of Cambridge Studies in Advanced Mathematics, 1997.

M. I. Krastanov and V. M. Veliov, Local controllability of state constrained linear systems, Acta Univ. Lodz., Folia Math, vol.5, pp.103-112, 1992.

M. I. Krastanov, On the constrained small-time controllability of linear systems, Automatica, vol.44, issue.9, pp.2370-2374, 2008.
DOI : 10.1016/j.automatica.2008.01.007

T. T. Le and A. Marigonda, Small-time local attainability for a class of control systems with state constraints, ESAIM Control Optim. Calc. Var, vol.23, issue.3, pp.1003-1021, 2017.

E. B. Lee and L. Markus, Foundations of optimal control theory. (The SIAM Series in Applied Mathematics, p.p, 1967.

J. Lohéac, E. Trélat, and E. Zuazua, Minimal controllability time for the heat equation under unilateral state or control constraints, Mathematical Models and Methods in Applied Sciences, vol.1, issue.09, pp.1587-1644, 2017.
DOI : 10.1016/S1874-5717(07)80010-7

J. Lohéac, E. Trélat, and E. Zuazua, Control of the semi-discrete heat equation under nonnegative control constraint

D. Pighin and E. Zuazua, Controllability under positivity constraints of semilinear heat equations, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01643062

Z. Rao and K. Kunisch, Minimal time problem with impulsive controls, Appl. Math. Optim, vol.75, issue.1, pp.75-97, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01107381

T. I. Seidman and J. Yong, How violent are fast controls?, II, Mathematics of Control, Signals, and Systems, vol.1, issue.4, pp.327-340, 1996.
DOI : 10.1007/978-3-642-61859-8

URL : http://www.math.umbc.edu/~seidman/Papers/ctrl_violent2.pdf

G. N. Silva and R. B. Vinter, Necessary Conditions for Optimal Impulsive Control Problems, SIAM Journal on Control and Optimization, vol.35, issue.6, pp.1829-1846, 1997.
DOI : 10.1137/S0363012995281857

E. D. Sontag, Mathematical control theory Deterministic finite dimensional systems, 1998.

E. Trélat, Contrôle optimal. Théorie et applications, 2005.

E. Trélat and E. Zuazua, The turnpike property in finite-dimensional nonlinear optimal control, Journal of Differential Equations, vol.258, issue.1, pp.81-114, 2015.
DOI : 10.1016/j.jde.2014.09.005

J. Warga, Optimal control of differential and functional equations, 1972.