A. Altarovici, O. Bokanowski, and H. Zidani, A general Hamilton-Jacobi framework for nonlinear state-constrained control problems. ESAIM: Control, Optimisation and Calculus of Variations, pp.337-357, 2013.
DOI : 10.1051/cocv/2012011

URL : https://hal.archives-ouvertes.fr/hal-00653337

A. V. Arutyunov and N. T. Tynyanskiy, The maximum principle in a problem with phase constraints, Soviet Journal of Computer and System Sciences, vol.23, pp.28-35, 1984.

A. V. Arutyunov, On Necessary Conditions for Optimality in a Problem with State Constraints, Dokl. Akad. Nauk SSSR, vol.280, issue.5, pp.1033-1037, 1985.

A. V. Arutyunov, On the theory of the maximum principle in optimal control problems with phase constraints, Soviet Math. Dokl, vol.39, issue.1, pp.1-4, 1989.

J. P. Aubin and A. Cellina, Differential inclusions: set-valued maps and viability theory of Grundlehren der mathematischen Wissenschaften, 1984.

M. Bardi and I. Capuzzo-dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi- Bellman equations. Systems & Control: Foundations & Applications, Birkhäuser Boston Inc, 1997.
DOI : 10.1007/978-0-8176-4755-1

R. C. Barnard and P. R. Wolenski, Flow invariance on stratified domains. Set-Valued and Variational Analysis, pp.377-403, 2013.
DOI : 10.1007/s11228-013-0230-y

URL : http://arxiv.org/abs/1208.4742

E. N. Barron and R. Jensen, Semicontinuous Viscosity Solutions For Hamilton???Jacobi Equations With Convex Hamiltonians, Communications in Partial Differential Equations, vol.10, issue.12, pp.1713-1742, 1990.
DOI : 10.1007/BF02765025

P. Bettiol, H. Frankowska, and R. B. , <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>L</mml:mi><mml:mo>???</mml:mo></mml:msup></mml:math> estimates on trajectories confined to a closed subset, Journal of Differential Equations, vol.252, issue.2, pp.1912-1933, 2012.
DOI : 10.1016/j.jde.2011.09.007

A. Blanc, Deterministic Exit Time Control Problems With Discontinuous Exit costs, SIAM Journal on Control and Optimization, vol.35, issue.2, pp.399-434, 1997.
DOI : 10.1137/S0363012994267340

O. Bokanowski, N. Forcadel, and H. Zidani, Deterministic state-constrained optimal control problems without controllability assumptions. ESAIM: Control, Optimisation and Calculus of Variations, pp.995-1015, 2011.
DOI : 10.1051/cocv/2010030

URL : https://hal.archives-ouvertes.fr/hal-00415953

F. Clarke, Functional analysis, calculus of variations and optimal control, Graduate Text in Mathematics, vol.264, 2013.
DOI : 10.1007/978-1-4471-4820-3

URL : https://hal.archives-ouvertes.fr/hal-00865914

F. Clarke, Y. Ledyaev, R. Stern, and P. Wolenski, Nonsmooth Analysis and Control Theory, Graduate Text in Mathematics, vol.178, 1998.
DOI : 10.1007/978-0-387-30440-3_370

URL : https://hal.archives-ouvertes.fr/hal-00863298

M. Crandall, L. Evans, and P. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, vol.282, issue.2, pp.487-502, 1984.
DOI : 10.1090/S0002-9947-1984-0732102-X

A. Y. Dubovitskii and V. A. Dubovitskii, Necessary conditions for strong minimum in optimal control problems with degeneration of endpoint and phase constraints, Usp. Mat. Nauk, vol.40, issue.2, pp.175-176, 1985.

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 : 10.1007/s00245-013-9193-5

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

H. Frankowska, Lower Semicontinuous Solutions of Hamilton???Jacobi???Bellman Equations, SIAM Journal on Control and Optimization, vol.31, issue.1, pp.257-272, 1993.
DOI : 10.1137/0331016

H. Frankowska and S. Plaskacz, Semicontinuous Solutions of Hamilton???Jacobi???Bellman Equations with Degenerate State Constraints, Journal of Mathematical Analysis and Applications, vol.251, issue.2, pp.818-838, 2000.
DOI : 10.1006/jmaa.2000.7070

H. Frankowska and R. B. Vinter, Existence of Neighboring Feasible Trajectories: Applications to Dynamic Programming for State-Constrained Optimal Control Problems, Journal of Optimization Theory and Applications, vol.35, issue.1, pp.20-40, 2000.
DOI : 10.1023/A:1004668504089

C. Hermosilla and H. Zidani, Infinite horizon problems on stratifiable state-constraints sets, Journal of Differential Equations, vol.258, issue.4, pp.1430-1460, 2015.
DOI : 10.1016/j.jde.2014.11.001

URL : https://hal.archives-ouvertes.fr/hal-00955921

H. Ishii and S. Koike, A New Formulation of State Constraint Problems for First-Order PDEs, SIAM Journal on Control and Optimization, vol.34, issue.2, pp.554-571, 1996.
DOI : 10.1137/S0363012993250268

J. Lee, Introduction to smooth manifolds, Graduate Text in Mathematics, vol.218, 2013.
DOI : 10.1007/978-0-387-21752-9

M. Motta, On Nonlinear Optimal Control Problems with State Constraints, SIAM Journal on Control and Optimization, vol.33, issue.5, pp.1411-1424, 1995.
DOI : 10.1137/S0363012993247445

M. Motta and F. Rampazzo, Multivalued dynamics on a closed domain with absorbing boundary. Applications to optimal control problems with integral constraints, Nonlinear Analysis: Theory, Methods & Applications, vol.41, issue.5-6, pp.631-647, 2000.
DOI : 10.1016/S0362-546X(98)00301-0

H. Soner, Optimal Control with State-Space Constraint I, SIAM Journal on Control and Optimization, vol.24, issue.3, pp.552-561, 1986.
DOI : 10.1137/0324032

H. Soner, Optimal Control with State-Space Constraint. II, SIAM Journal on Control and Optimization, vol.24, issue.6, pp.1110-1122, 1986.
DOI : 10.1137/0324067

G. Smirnov, Introduction to the theory of differential inclusions, Graduate Studies in Mathematics. AMS, vol.41, 2002.
DOI : 10.1090/gsm/041

P. Wolenski and Y. Zhuang, Proximal Analysis and the Minimal Time Function, SIAM Journal on Control and Optimization, vol.36, issue.3, pp.1048-1072, 1998.
DOI : 10.1137/S0363012996299338