V. (. Arutyunov, L. Dykhta, and . 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

I. (. Bardi and . Capuzzo-dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems and Control: Foundations and Applications, 1997.

. (. Barles, Solutions de viscosité deséquationsdeséquations de Hamilton- Jacobi, Mathématiques et Applications, vol.17, 1994.

. (. 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

P. (. Barles and . 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

. (. Barron, Viscosity solutions and analysis in L ? . Nonlinear analysis, differential equations and control, NATO Sci. Ser. C Math. Phys. Sci, vol.528, pp.1-60, 1998.
DOI : 10.1007/978-94-011-4560-2_1

R. (. Barron and . 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

J. Baumeister, On optimal control of a fishery, Proceedings of NOLCOS'01, volume 5th IFAC Symposium on Nonlinear Control Systems, 2001.

O. Bokanowski, E. Cristiani, J. Laurent-varin, and H. Zidani, Hamilton- Jacobi-Bellman approach for the climbing problem. preprint submitted
URL : https://hal.archives-ouvertes.fr/hal-00537649

A. Bressan, On differential systems with impulsive controls, Rend. Sem. Mat. Univ. Padova, vol.78, issue.10, pp.227-236, 1987.

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

F. (. Bressan and . 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. Briani, A Hamilton-Jacobi equation with measures arising in ?-convergence of optimal control problems, Differential and Integral Equations, vol.12, issue.6, pp.849-886, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00975011

F. (. Briani and . Rampazzo, A density approach to Hamilton-Jacobi equations with t-measurable Hamiltonians, NoDEA-Nonlinear Differential equations and Applications, pp.71-92, 2005.
DOI : 10.1007/s00030-004-2030-4

URL : https://hal.archives-ouvertes.fr/hal-00977791

. (. Brogliato, Nonsmooth impact Mechanics: Models, Dynamics and control, Lecture Notes in Control and Information Sciences, vol.220, 1996.

C. Clark, F. Clarke, and G. Munro, The Optimal Exploitation of Renewable Resource Stocks: Problems of Irreversible Investment, Econometrica, vol.47, issue.1, pp.25-47, 1979.
DOI : 10.2307/1912344

F. (. Dal-maso and . Rampazzo, On systems of ordinary differential equations with measures as controls, Differential and Integral Equations, pp.738-765, 1991.

O. (. Dykhta and . Samsonyuk, Optimal impulse control with applications, Nauka, 1991.

. (. 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

S. (. Frankowska and . Plaskacz, A measurable upper semicontinuous viability theorem for tubes, Nonlinear Analysis: Theory, Methods & Applications, vol.26, issue.3, pp.565-582, 1996.
DOI : 10.1016/0362-546X(94)00299-W

S. (. Frankowska, T. Plaskacz, and . Rzeuchowski, 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

C. (. Gajardo, A. Ramírez, and . Rappaport, Minimal Time Sequential Batch Reactors with Bounded and Impulse Controls for One or More Species, SIAM Journal on Control and Optimization, vol.47, issue.6, pp.2827-2856, 2008.
DOI : 10.1137/070695204

URL : https://hal.archives-ouvertes.fr/hal-00857823

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

B. (. Lions and . Perthame, Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians. Nonlinear analysis, Theory, Methods & Applications, vol.11, issue.5, pp.613-612, 1987.

. (. Miller, Optimization of dynamic systems with a generalized control, Automation and Remote Control, vol.50, 1989.

. (. Monteillet, Convergence of approximation schemes for nonlocal front propagation equations, Mathematics of Computation, vol.79, issue.269, pp.125-146, 2010.
DOI : 10.1090/S0025-5718-09-02270-4

URL : https://hal.archives-ouvertes.fr/hal-00326624

J. Raymond, Optimal control problems in spaces of functions of bounded variation, Differential Integral Equations, vol.10, pp.105-136, 1997.

A. V. Sarychev, Nonlinear systems with impulsive and generalised functions controls, Proc. Conf. on NONlinear Synthesis, 1989.

. (. Sussmann, On the Gap Between Deterministic and Stochastic Ordinary Differential Equations, The Annals of Probability, vol.6, issue.1, pp.17-41, 1978.
DOI : 10.1214/aop/1176995608