Y. Achdou, F. Camilli, A. Cutr-`-cutr-`-i, and N. Tchou, Hamilton???Jacobi equations constrained on networks, Nonlinear Differential Equations and Applications NoDEA, vol.62, issue.1, pp.413-445, 2013.
DOI : 10.1007/s00030-012-0158-1

URL : https://hal.archives-ouvertes.fr/hal-00656919

Y. Achdou, S. Oudet, and N. Tchou, Hamilton???Jacobi equations for optimal control on junctions and networks, ESAIM: Control, Optimisation and Calculus of Variations, vol.21, issue.3, pp.876-899, 2015.
DOI : 10.1051/cocv/2014054

URL : https://hal.archives-ouvertes.fr/hal-00847210

A. Altarovici, O. Bokanowski, and H. Zidani, A general Hamilton-Jacobi framework for non-linear state-constrained control problems, ESAIM: Control, Optimisation and Calculus of Variations, vol.19, issue.2, pp.337-357, 2013.
DOI : 10.1051/cocv/2012011

J. Aubin and A. Cellina, Differential inclusions: set-valued maps and viability theory, volume 264 of Grundlehren der mathematischen Wissenschaften, 1984.

J. Aubin and H. Frankowska, Set-Valued Analysis. Systems & Control: Foundations & Applications, 1990.

M. Bardi and I. Capuzzo-dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems & Control: Foundations & Applications, Birkhäuser Boston Inc, 1997.

G. Barles, A. Briani, and E. Chasseigne, A Bellman approach for two-domains optimal control problems in R n . ESAIM: Control, Optimisation and Calculus of Variations, pp.710-739, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00652406

G. Barles, A. Briani, and E. Chasseigne, A Bellman Approach for Regional Optimal Control Problems in $\mathbb{R}^N$, SIAM Journal on Control and Optimization, vol.52, issue.3, pp.1712-1744, 2014.
DOI : 10.1137/130922288

F. Camilli, A. Festa, and D. Schieborn, An approximation scheme for a Hamilton???Jacobi equation defined on a network, Applied Numerical Mathematics, vol.73, pp.33-47, 2013.
DOI : 10.1016/j.apnum.2013.05.003

URL : https://hal.archives-ouvertes.fr/hal-00724768

P. Cardaliaguet, M. Quincampoix, and P. Saint-pierre, Optimal times for constrained nonlinear control problems without local controllability, Applied Mathematics & Optimization, vol.8, issue.2, pp.21-42, 1997.
DOI : 10.1007/BF02683336

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

H. Frankowska and R. B. Vinter, Existence of neighbouring feasible trajectories: applications to dynamic programming for state constrained optimal control problems, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), pp.20-40, 2000.
DOI : 10.1109/CDC.2001.914654

C. Hermosilla, Stratified discontinuous differential equations and sufficient conditions for robustness, Discrete and Continuous Dynamical Systems, vol.35, issue.9, pp.4415-4437, 2015.
DOI : 10.3934/dcds.2015.35.4415

URL : https://hal.archives-ouvertes.fr/hal-00955927

C. Hermosilla, P. Wolenski, and H. Zidani, The Mayer and minimum time problems with stratified state constraints, 2015.

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

C. Imbert and R. Monneau, Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks. preprint, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00832545

C. Imbert and R. Monneau, Quasi-convex Hamilton-Jacobi equations posed on junctions: the multidimensional case. arXiv preprint arXiv:1410, p.3056, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01073954

C. Imbert, R. Monneau, and H. Zidani, A Hamilton-Jacobi approach to junction problems and application to traffic flows. ESAIM: Control, Optimisation and Calculus of Variations, pp.129-166, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00569010

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.

G. Leoni, A first course in Sobolev spaces, American Mathematical Soc, vol.105, 2009.
DOI : 10.1090/gsm/105

S. Oudet, Hamilton-Jacobi equations for optimal control on multidimensional junctions. arXiv preprint arXiv, pp.1412-2679, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01093112

Z. Rao, A. Siconolfi, and H. Zidani, Transmission conditions on interfaces for Hamilton???Jacobi???Bellman equations, Journal of Differential Equations, vol.257, issue.11, pp.3978-4014, 2014.
DOI : 10.1016/j.jde.2014.07.015

URL : https://hal.archives-ouvertes.fr/hal-00820273

Z. Rao and H. Zidani, Hamilton???Jacobi???Bellman Equations on Multi-domains, Control and Optimization with PDE Constraints, pp.93-116, 2013.
DOI : 10.1007/978-3-0348-0631-2_6

URL : https://hal.archives-ouvertes.fr/hal-00803108

R. T. Rockafellar, Proximal Subgradients, Marginal Values, and Augmented Lagrangians in Nonconvex Optimization, Mathematics of Operations Research, vol.6, issue.3, pp.424-436, 1981.
DOI : 10.1287/moor.6.3.424

D. Schieborn and F. Camilli, Viscosity solutions of Eikonal equations on topological networks, Calculus of Variations and Partial Differential Equations, vol.291, issue.12, pp.3-4, 2013.
DOI : 10.1007/s00526-012-0498-z

URL : https://hal.archives-ouvertes.fr/hal-00724761

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

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

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