Y. Achdou, F. Camilli, A. Cutri, and A. 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

A. Altarovici, O. Bokanowski, and A. 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

O. Alvarez and A. M. Bardi, Viscosity Solutions Methods for Singular Perturbations in Deterministic and Stochastic Control, SIAM Journal on Control and Optimization, vol.40, issue.4, pp.1159-1188, 2001.
DOI : 10.1137/S0363012900366741

O. Alvarez and A. M. Bardi, Singular Perturbations of Nonlinear Degenerate Parabolic PDEs: a General Convergence Result, Archive for Rational Mechanics and Analysis, vol.170, issue.1, pp.17-61, 2003.
DOI : 10.1007/s00205-003-0266-5

O. Alvarez, M. Bardi, and A. C. Marchi, MULTISCALE SINGULAR PERTURBATIONS AND HOMOGENIZATION OF OPTIMAL CONTROL PROBLEMS, Series of Advances in Mathematics for Applied Sciences, pp.1-27, 2008.
DOI : 10.1142/9789812776075_0001

M. Amar, G. Crasta, and A. A. Malusa, On the Finsler metrics obtained as limits of chessboard structures, Advances in Calculus of Variations, vol.2, issue.4, pp.321-360, 2009.
DOI : 10.1515/ACV.2009.013

Z. Artstein, The chattering limit of singularly perturbed optimal control problems, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), pp.564-569, 2000.
DOI : 10.1109/CDC.2000.912824

Z. Artstein, An occupational measure solution to a singularly perturbed optimal control problem, Control Cybernet, vol.31, pp.623-642, 2002.

Z. Artstein and A. V. Gaitsgory, Tracking Fast Trajectories Along a Slow Dynamics: A Singular Perturbations Approach, SIAM Journal on Control and Optimization, vol.35, issue.5, pp.1487-1507, 1997.
DOI : 10.1137/S036301299528458X

Z. Artstein and A. V. Gaitsgory, The value function of singularly perturbed control systems, Appl. Math. Anal. Appl, vol.41, pp.425-445, 2000.

Z. Artstein and A. V. Gaitsgory, Convergence to convex compact sets in infinite dimensions, Journal of Mathematical Analysis and Applications, vol.284, issue.2, pp.471-480, 2003.
DOI : 10.1016/S0022-247X(03)00334-2

Z. Artstein and A. A. Leizarowitz, Singularly Perturbed Control Systems with One-Dimensional Fast Dynamics, SIAM Journal on Control and Optimization, vol.41, issue.2, pp.641-658, 2002.
DOI : 10.1137/S0363012901390889

A. Arutyunov, V. Dykhta, and A. Pereira, Necessary Conditions for Impulsive Nonlinear Optimal Control Problems without a priori Normality Assumptions, Journal of Optimization Theory and Applications, vol.9, issue.1, pp.55-77, 2005.
DOI : 10.1007/s10957-004-6465-x

J. Aubin and A. A. Frankowska, Set-valued analysis

F. Bagagiolo and A. M. Bardi, Singular Perturbation of a Finite Horizon Problem with State-Space Constraints, SIAM Journal on Control and Optimization, vol.36, issue.6, pp.2040-2060, 1998.
DOI : 10.1137/S0363012996314476

F. Bagagiolo and A. K. Danieli, Infinite horizon optimal control problems with multiple thermostatic hybrid dynamics, Nonlinear Analysis: Hybrid Systems, pp.824-838, 2012.

M. Bardi and A. , Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Systems and Control: Foundations and Applications, 1997.

G. Barles, Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations: a guided visit, Nonlinear Analysis: Theory, Methods & Applications, vol.20, issue.9, pp.1123-1134, 1993.
DOI : 10.1016/0362-546X(93)90098-D

G. Barles, Solution de viscosité des équations de Hamilton-Jacobi, Mathématiques et Applications, vol.17, 1994.

G. Barles, A new stability result for viscosity solutions of nonlinear parabolic equations with weak convergence in time, Comptes Rendus Mathematique, vol.343, issue.3, pp.173-178, 2006.
DOI : 10.1016/j.crma.2006.06.022

URL : https://hal.archives-ouvertes.fr/hal-00016437

G. Barles, A. Briani, and A. E. Chasseigne, A Bellman approach for regional optimal control problems in R N , preprint

G. Barles, S. Dharmatti, and A. M. Ramaswamy, Unbounded viscosity solutions of hybrid control systems, ESAIM: Control, Optimisation and Calculus of Variations, vol.16, issue.1, pp.176-193, 2010.
DOI : 10.1051/cocv:2008076

URL : https://hal.archives-ouvertes.fr/hal-00255763

G. Barles and A. E. Jakobsen, On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations, ESAIM: M2AN, pp.33-54, 2002.

G. Barles and A. B. Perthame, Discontinuous solutions of deterministic optimal stopping time problems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.21, issue.4, pp.557-579, 1987.
DOI : 10.1051/m2an/1987210405571

G. Barles and A. P. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, 29th IEEE Conference on Decision and Control, pp.271-283, 1991.
DOI : 10.1109/CDC.1990.204046

R. C. Barnard and A. P. Wolenski, Flow invariance on stratified domains, Set-Valued and Variational Analysis, pp.377-403, 2013.

E. N. Barron, Viscosity solutions and analysys in L +?, Proceedings of the NATO advanced Study Institute, pp.1-60, 1999.

E. N. Barron and A. 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

E. N. Barron and A. R. Jensen, Optimal control and semicontinuous viscosity solutions, Proc. Amer, pp.49-79, 1991.
DOI : 10.1090/S0002-9939-1991-1076572-8

J. Bechhofer and A. B. Johnson, A simple model for Faraday waves, American Journal of Physics, vol.64, issue.12, pp.1482-1487, 1996.
DOI : 10.1119/1.18412

A. Bensoussan, Perturbation Methods in Optimal control, 1988.

P. Bettiol, A. Bressan, and A. R. Vinter, On Trajectories Satisfying a State Constraint: $W^{1,1}$ Estimates and Counterexamples, SIAM Journal on Control and Optimization, vol.48, issue.7, pp.4664-4679, 2010.
DOI : 10.1137/090769788

P. Bettiol, H. Frankowska, A. R. Vinter, and L. ?. , <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 A. H. Zidani, Reachability and Minimal Times for State Constrained Nonlinear Problems without Any Controllability Assumption, SIAM Journal on Control and Optimization, vol.48, issue.7, pp.4292-4316, 2010.
DOI : 10.1137/090762075

URL : https://hal.archives-ouvertes.fr/hal-00395589

O. Bokanowski, N. Forcadel, and A. H. Zidani, Deterministic state-constrained optimal control problems without controllability assumptions, ESAIM: Control, Optimisation and Calculus of Variations, vol.17, issue.4, pp.975-994, 2011.
DOI : 10.1051/cocv/2010030

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

B. Bouchard and A. N. Dang, Optimal Control vs Stochastic Target problems: An Equivalence Result, pp.343-346, 2012.

M. S. Branicky, V. S. Borkar, and S. K. Mitter, A unified framework for hybrid control: model and optimal control theory, IEEE Transactions on Automatic Control, vol.43, issue.1
DOI : 10.1109/9.654885

A. Bressan, Impulsive Control Systems, Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control, pp.1-22, 1996.
DOI : 10.1007/978-1-4613-8489-2_1

A. Bressan, Errata corrige, Networks and Heterogeneous Media, vol.8, issue.2, p.625, 2013.
DOI : 10.3934/nhm.2013.8.625

A. Bressan and A. Y. Hong, Optimal control problems for control systems on stratified domains, Network and Heterogeneous Media, pp.313-331, 2007.

A. Bressan and A. F. Rampazzo, On differential systems with vector-valued impulsive controls, Boll. Unione Mat. Ital, vol.7, issue.2, pp.641-656, 1988.

A. Bressan and A. F. Rampazzo, Impulsive control systems without commutativity assumptions, Journal of Optimization Theory and Applications, vol.8, issue.3, pp.67-83, 1991.
DOI : 10.1007/BF02193094

A. Bressan and A. F. Rampazzo, Impulsive control systems without commutativity assumptions, Journal of Optimization Theory and Applications, vol.8, issue.3, pp.435-457, 1994.
DOI : 10.1007/BF02193094

A. Briani and . Hamilton, Jacobi equation with measures arising in ?-convergence of optimal control problems, Differential and Integral Equations, pp.849-886, 1999.

A. Briani and A. A. Davini, Monge solutions for discontinuous Hamiltonians, ESAIM. Control, Optimisation and Calculus of Variations, pp.229-251, 2005.
DOI : 10.1051/cocv:2005004

URL : http://archive.numdam.org/article/COCV_2005__11_2_229_0.pdf

A. Briani and A. H. Zidani, Characterization of the value function of final state constrained control problems with BV trajectories, Communications on Pure and Applied Analysis, vol.10, issue.6, pp.1567-1587, 2011.
DOI : 10.3934/cpaa.2011.10.1567

URL : https://hal.archives-ouvertes.fr/inria-00627518

B. Brogliato, Nonsmooth Impact Mechanics: Models, Dynamics and Control, lecture notes in Control and Information Sciences, 1996.

F. Camilli and A. Siconolfi, Hamilton-Jacobi equations with measurable dependence on the state variable Advances in Differential Equations, pp.733-768, 2003.

F. Camilli and A. A. Siconolfi, Effective Hamiltonian and Homogenization of Measurable Eikonal Equations, Archive for Rational Mechanics and Analysis, vol.56, issue.1, pp.1-20, 2007.
DOI : 10.1007/s00205-006-0001-0

F. Camilli and A. Siconolfi, Time-Dependent Measurable Hamilton???Jacobi Equations, Communications in Partial Differential Equations, vol.51, issue.5-6, pp.813-847, 2005.
DOI : 10.1081/PDE-200059292

P. Cannarsa and A. C. Sinestrari, Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control Progress in nonlinear differential equations and their applications, 2004.

F. H. Clarke, Optimization and Nonsmooth Analysis, Classics in Applied Mathematics, SIAM, vol.5, 1983.
DOI : 10.1137/1.9781611971309

F. H. Clarke, Methods of Dynamic and Nonsmooth Optimization, CBMS/NSF Regional Conf. Ser. in Appl. Math, vol.57, 1989.
DOI : 10.1137/1.9781611970142

F. H. Clarke, Y. S. Ledyaev, R. J. Stern, and A. P. Wolenski, Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics, vol.178
DOI : 10.1007/978-1-4614-1806-1_69

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

F. H. Clarke, Y. S. Ledyaev, R. J. Stern, and A. P. Wolenski, Qualitative properties of trajectories of control systems: A survey, Journal of Dynamical and Control Systems, vol.20, issue.No. 2, 1995.
DOI : 10.1007/BF02254655

M. Crandall, L. Evans, and A. 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

M. Crandall, H. Ishii, and A. Lions, user's guide to viscosity solutions\\ of second order\\ partial differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

I. Capuzzo-dolchetta and A. Lions, Hamilton-Jacobi equations with state constraints, Transactions of the American Mathematical Society, vol.318, issue.2, pp.643-683, 1990.
DOI : 10.1090/S0002-9947-1990-0951880-0

M. Crandall and A. Lions, Conditions d'unicité pour les solutions généralises des équations d'Hamilton-Jacobi du premier ordre, C. R. Acad. Sci. Paris Sér. I Math, vol.292, pp.487-502, 1981.

M. Crandall and A. Lions, Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, vol.277, issue.1, pp.1-42, 1983.
DOI : 10.1090/S0002-9947-1983-0690039-8

A. Catlla, J. Porter, and A. M. Silber, Weakly nonlinear analysis of impulsively-forced Faraday waves, Physical Review E, vol.72, issue.5, 2005.
DOI : 10.1103/PhysRevE.72.056212

A. Catlla, D. Schaeffer, T. Witelski, E. Monson, and A. A. Lin, On Spiking Models for Synaptic Activity and Impulsive Differential Equations, SIAM Review, vol.50, issue.3, pp.553-569, 2005.
DOI : 10.1137/060667980

M. C. Delfour and J. P. Zolésio, Shape Analysis via Oriented Distance Functions, Journal of Functional Analysis, vol.123, issue.1, pp.129-201, 1994.
DOI : 10.1006/jfan.1994.1086

URL : http://doi.org/10.1006/jfan.1994.1086

G. Maso and A. F. Rampazzo, On systems of ordinary differential equations with measures as controls, Differential and Integral Equations, pp.738-765, 1991.

M. C. Delfour and A. J. Zolésio, Shape Analysis via Oriented Distance Functions, Journal of Functional Analysis, vol.123, issue.1, pp.129-201, 1994.
DOI : 10.1006/jfan.1994.1086

URL : http://doi.org/10.1006/jfan.1994.1086

D. Zan and A. P. Soravia, Cauchy problems for noncoercive Hamilton-Jacobi-Issacs equations with discontinuous coefficiens, Interfaces Free Bound, pp.347-368, 2010.

P. Dupuis, A numerical method for a calculus of variations problem with discontinuous integrand, Lecture notes in Control and Inform. Sci, vol.177, pp.90-107, 1991.
DOI : 10.1007/BFb0007050

L. C. Evans, Synopsis, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.120, issue.3-4, pp.245-265, 1992.
DOI : 10.1090/S0002-9947-1983-0690039-8

A. F. Filippov, Differential equations with discontinuous right-hand side, 1988.
DOI : 10.1090/trans2/042/13

N. Forcadel and Z. , Rao Singular perturbation of optimal control problems on multidomains , submitted

N. Forcadel, Z. Rao, and H. , Zidani Optimal control problems of BV trajectories with pointwise state constraints, Proceedings of the 18th IFAC World Congress, pp.2583-2588, 2011.

N. Forcadel, Z. Rao, and H. , 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, Hamilton-Jacobi equations: Viscosity solutions and generalized gradients, Journal of Mathematical Analysis and Applications, vol.141, issue.1, pp.21-26, 1989.
DOI : 10.1016/0022-247X(89)90203-5

URL : http://doi.org/10.1016/0022-247x(89)90203-5

H. Frankowska, Optimal trajectories associated with a solution of the contingent Hamilton-Jacobi equation, Applied Mathematics & Optimization, vol.23, issue.4, pp.291-311, 1989.
DOI : 10.1007/BF01448202

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 A. M. Mazzola, On relations of the adjoint state to the value function for optimal control problems with state constraints, Nonlinear Differential Equations and Applications NoDEA, vol.1, issue.2
DOI : 10.1007/s00030-012-0183-0

URL : https://hal.archives-ouvertes.fr/hal-00800199

H. Frankowska and A. S. Plaskacz, Semicontinuous solutions of

H. Frankowska, S. Plaskacz, and A. T. Rzezuchowski, Measurable Viability Theorems and the Hamilton-Jacobi-Bellman Equation, Journal of Differential Equations, vol.116, issue.2, pp.265-305, 1995.
DOI : 10.1006/jdeq.1995.1036

H. Frankowska and A. R. 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
DOI : 10.1023/A:1004668504089

A. Fathi and A. A. Siconolfi, PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians, Calculus of Variations, vol.24, issue.2, pp.185-228, 2005.
DOI : 10.1007/s00526-004-0271-z

W. H. Fleming and A. H. Soner, Controlled Markov processes and viscosity solutions, 1993.

V. Gaitsgory, Suboptimization of Singularly Perturbed Control Systems, SIAM Journal on Control and Optimization, vol.30, issue.5, pp.1228-1249, 1992.
DOI : 10.1137/0330065

V. Gaitsgory, On a Representation of the Limit Occupational Measures Set of a Control System with Applications to Singularly Perturbed Control Systems, SIAM Journal on Control and Optimization, vol.43, issue.1, pp.325-340, 2004.
DOI : 10.1137/S0363012903424186

V. Gaitsgory and A. A. Leizarowitz, Limit Occupational Measures Set for a Control System and Averaging of Singularly Perturbed Control Systems, Journal of Mathematical Analysis and Applications, vol.233, issue.2, pp.461-475, 1999.
DOI : 10.1006/jmaa.1999.6281

V. Gaitsgory and A. M. Quincampoix, Linear Programming Approach to Deterministic Infinite Horizon Optimal Control Problems with Discounting, SIAM Journal on Control and Optimization, vol.48, issue.4, pp.2480-2512, 2009.
DOI : 10.1137/070696209

V. Gaitsgory and A. S. Rossomakhine, Linear Programming Approach to Deterministic Long Run Average Problems of Optimal Control, SIAM Journal on Control and Optimization, vol.44, issue.6, pp.2006-2037, 2006.
DOI : 10.1137/040616802

Y. Giga, P. Górka, and P. Rybka, A comparison principle for Hamilton-Jacobi equations with discontinuous Hamiltonians, Proc. Amer, pp.1777-1785, 2011.
DOI : 10.1090/S0002-9939-2010-10630-5

M. Garavello and A. P. Soravia, Optimality principles and uniqueness for Bellman equations of unbounded control problems with discontinuous running cost, Nonlinear Differential Equations and Applications NoDEA, vol.11, issue.3, pp.271-298, 2004.
DOI : 10.1007/s00030-004-1058-9

M. Garavello and A. P. Soravia, Representation Formulas for Solutions of the HJI Equations with Discontinuous Coefficients and Existence of Value in Differential Games, Journal of Optimization Theory and Applications, vol.11, issue.2, pp.209-229, 2006.
DOI : 10.1007/s10957-006-9099-3

G. Granato and H. Zidani, Reachability of delayed hybrid systems using level-set methods, submitted

J. Guckenheimer and A. P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 1990.

C. Hsu and A. W. Cheng, Applications of the Theory of Impulsive Parametric Excitation and New Treatments of General Parametric Excitation Problems, Journal of Applied Mechanics, vol.40, issue.1, pp.551-558, 1973.
DOI : 10.1115/1.3422976

C. Huepe, Y. Ding, P. Umbanhowar, and A. M. Silber, Forcing function control of Faraday wave instabilities in viscous shallow fluides, Phys. Rev. E, vol.73, 2006.

H. Ishii, Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets. I, Bull, Facul. Sci. Eng, vol.28, pp.33-77, 1985.

H. Ishii, Perron's method for Hamilton-Jacobi equations, Duke Math, J, vol.55, pp.369-384, 1987.

H. Ishii, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations, Ann. Sc. Norm. Sup. Pisa (IV), vol.16, pp.105-135, 1989.

H. Ishii and A. 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

C. Imbert, R. Monneau, A. H. Zidani, and . Hamilton, A Hamilton-Jacobi approach to junction problems and application to traffic flows, ESAIM: Control, Optimisation and Calculus of Variations, vol.19, issue.1, pp.129-166, 2013.
DOI : 10.1051/cocv/2012002

URL : https://hal.archives-ouvertes.fr/hal-00569010

P. Kokotovi?, H. Khalil, and A. J. Reilly, Singular Perturbation Methods in Control: Analysis and Design, 1986.
DOI : 10.1137/1.9781611971118

S. Krantz and A. H. Park, Distance to Ck hypersurfaces, Journal of Differential Equations, vol.40, issue.1, pp.116-120, 1981.
DOI : 10.1016/0022-0396(81)90013-9

URL : http://doi.org/10.1016/0022-0396(81)90013-9

P. L. Lions and A. B. Perthame, Remarks on Hamilton-Jacobi equations with measurable time-dependant Hamiltonians, Nonlinear analysis, Theory, Methods Applications, pp.613-612, 1987.

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 A. F. Rampazzo, Dynamical programming for nonlinear systems driven by ordinary and impulsive controls, SIAM J. Control Optim, vol.44, issue.1, pp.199-225, 1996.

J. Mcshane, R. B. Warfield, and J. , On Filippov's implicit functions lemma, Proc. Amer, pp.41-47, 1967.

R. T. Newcomb and J. Su, Eikonal equations with discontinuities, Differential and Integral equations, pp.1947-1960, 1995.

A. M. Oberman, R. Takei, and A. A. Vladimirsky, Homogenization of metric Hamilton- Jacobi equations, Multiscale Modeling and Simulation, pp.269-295, 2009.

M. Quincampoix and A. F. Watbled, Averaging method for discontinuous Mayer's problem of singularly perturbed control systems, Nonlinear Analysis: Theory, Methods & Applications, vol.54, issue.5, pp.819-837, 2003.
DOI : 10.1016/S0362-546X(03)00094-4

M. Quincampoix and A. H. Zhang, Singular perturbations in non-linear optimal control systems, Differential and Integral Equations, vol.8, issue.4, pp.931-944, 1995.

J. Raymond, Optimal control problems in spaces of functions of bounded variation. I, Differential Integral Equations, pp.105-136, 1997.

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

Z. Rao, A. Siconolfi, and A. , Zidani Transmission conditions on interfaces for Hamilton-Jacobi-Bellman equations, submitted

Z. Rao and A. H. Zidani, Hamilton-Jacobi-Bellman equations on multi-domains, Control and Optimization with PDE Constraints, International Series of Numerical Mathematics, vol.164, pp.93-116, 2013.

G. N. Silva and A. R. Vinter, Measure Driven Differential Inclusions, Journal of Mathematical Analysis and Applications, vol.202, issue.3, pp.746-767, 1996.
DOI : 10.1006/jmaa.1996.0344

URL : http://doi.org/10.1006/jmaa.1996.0344

G. N. Silva and A. R. Vinter, Necessary Conditions for Optimal Impulsive Control Problems, SIAM Journal on Control and Optimization, vol.35, issue.6, pp.1829-1846, 1998.
DOI : 10.1137/S0363012995281857

H. M. 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. M. 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. Soravia, Optimality priciples and representation formulas for viscosity solutions of Hamilton-Jacobi equations. II. equations of control problems with state constraints, Diff. and Int. Equations, vol.12, pp.275-293, 1999.

P. Soravia, Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian, Indiana University Mathematics Journal, vol.51, issue.2, pp.451-477, 2002.
DOI : 10.1512/iumj.2002.51.2105

P. Soravia, Degenerate Eikonal equations with discontinuous refraction index, ESAIM: Control, Optimisation and Calculus of Variations, vol.12, issue.2, pp.216-230, 2006.
DOI : 10.1051/cocv:2005033

URL : http://www.numdam.org/article/COCV_2006__12_2_216_0.pdf

A. J. Van-der-schaft and A. J. Schumacher, An introduction to hybrid dynamical systems, Lecture Notes in Control and Information Sciences, vol.251, 2000.
DOI : 10.1007/BFb0109998

P. R. Wolenski and A. S. Zabic, A differential solution concept for impulsive systems, Differ. Equ. Dyn. Syst, vol.2, pp.199-210, 2006.

P. R. Wolenski and A. S. Zabic, A Sampling Method and Approximation Results for Impulsive Systems, SIAM Journal on Control and Optimization, vol.46, issue.3, pp.983-998, 2007.
DOI : 10.1137/040620734

H. Zhang and M. R. James, Optimal Control of Hybrid Systems and a System of Quasi-Variational Inequalities, SIAM Journal on Control and Optimization, vol.45, issue.2, pp.722-761, 2005.
DOI : 10.1137/050630131