E. J. Anderson and P. Nash, Linear Programming in Infinite-Dimensional Spaces, 1987.

R. Beals, B. Gaveau, and P. C. Greiner, Hamilton???Jacobi theory and the heat kernel on Heisenberg groups, Journal de Math??matiques Pures et Appliqu??es, vol.79, issue.7, pp.633-689, 2000.
DOI : 10.1016/S0021-7824(00)00169-0

C. Berg, The multidimensional moment problem and semigroups, Proc. Symp, pp.110-124, 1987.
DOI : 10.1090/psapm/037/921086

A. G. Bhatt and V. S. Borkar, Occupation measures for controlled Markov processes: characterization and optimality, Ann. Probab, vol.24, pp.1531-1562, 1996.

V. Borkar, Convex Analytic Methods in Markov Decision Processes, pp.377-408, 2002.
DOI : 10.1007/978-1-4615-0805-2_11

O. Bokanowski, S. Martin, R. Munos, and H. Zidani, An anti-diffusive scheme for viability problems, Applied Numerical Mathematics, vol.56, issue.9, pp.56-1147, 2006.
DOI : 10.1016/j.apnum.2006.03.004

URL : https://hal.archives-ouvertes.fr/hal-00112062

R. W. Brockett, Asymptotic stability and feedback stabilization In: Differential geometric control theory, pp.181-191, 1983.

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

M. Cho, R. H. Jung, and . Stockbridge, Linear Programming Formulation for Optimal Stopping Problems, SIAM Journal on Control and Optimization, vol.40, issue.6, pp.1965-1982, 2002.
DOI : 10.1137/S0363012900377663

C. Coatmélec, Approximation et interpolation des fonctions différentiables de plusieurs variables Annales Scientifiques de l'Ecole Normale Supérieure, 3` eme série, pp.271-341, 1966.

D. A. Dawson, Qualitative behavior of geostochastic systems, Stochastic Processes and their Applications, vol.10, issue.1, pp.1-31, 1980.
DOI : 10.1016/0304-4149(80)90002-2

W. H. Fleming and D. Vermes, Convex Duality Approach to the Optimal Control of Diffusions, SIAM Journal on Control and Optimization, vol.27, issue.5, pp.1136-1155, 1989.
DOI : 10.1137/0327060

R. Fletcher, Practical methods of optimization Unconstrained optimization, 1980.

V. Gaitsgory and 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

P. E. Gill, W. Murray, and M. H. Wright, Practical optimization, 1981.

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

K. Helmes and R. H. Stockbridge, Numerical Comparison of Controls and Verification of Optimality for Stochastic Control Problems, Journal of Optimization Theory and Applications, vol.4, issue.1, pp.107-127, 2000.
DOI : 10.1023/A:1004659107996

K. Helmes, S. Röhl, and R. H. Stockbridge, Computing Moments of the Exit Time Distribution for Markov Processes by Linear Programming, Operations Research, vol.49, issue.4, pp.516-530, 2001.
DOI : 10.1287/opre.49.4.516.11221

D. Henrion and J. B. Lasserre, Feature - How gloptipoly is applied to problems in robust and nonlinear control Solving nonconvex optimization problems, IEEE Control Systems Magazine, vol.24, issue.3, pp.72-83, 2004.
DOI : 10.1109/MCS.2004.1299534

O. Hernández-lerma and J. B. Lasserre, Discrete-Time Markov Control Processes: Basic Optimality Criteria, 1996.
DOI : 10.1007/978-1-4612-0729-0

O. Hernández-lerma and J. B. Lasserre, Further Topics in Discrete-Time Markov Control Processes, 1999.
DOI : 10.1007/978-1-4612-0561-6

O. Hernández-lerma and J. B. Lasserre, Markov Chains and Invariant Probabilities, 2003.
DOI : 10.1007/978-3-0348-8024-4

O. Hernández-lerma and J. B. Lasserre, Approximation Schemes for Infinite Linear Programs, SIAM Journal on Optimization, vol.8, issue.4, pp.973-988, 1998.
DOI : 10.1137/S1052623497315768

O. Hernández-lerma and J. B. Lasserre, The linear programming approach, In: Hanbook of Markov Decision Processes, pp.377-408, 2002.

D. Hernandez-hernandez, O. Hernández-lerma, and M. Taksar, The linear programming approach to deterministic optimal control problems, Appl. Math, vol.24, pp.17-33, 1996.

M. W. Hirsch, Differential topology, Graduate Texts in Mathematics, vol.33, 1976.
DOI : 10.1007/978-1-4684-9449-5

D. Jacobson, M. Lele, and J. L. Speyer, New necessary conditions of optimality for control problems with state-variable inequality constraints, Journal of Mathematical Analysis and Applications, vol.35, issue.2, pp.255-284, 1971.
DOI : 10.1016/0022-247X(71)90219-8

J. L. Krivine, Anneaux pr??ordonn??s, Journal d'Analyse Math??matique, vol.12, issue.1, pp.307-326, 1964.
DOI : 10.1007/BF02807438

T. G. Kurtz and R. H. Stockbridge, Existence of Markov Controls and Characterization of Optimal Markov Controls, SIAM Journal on Control and Optimization, vol.36, issue.2, pp.609-653, 1998.
DOI : 10.1137/S0363012995295516

J. B. Lasserre, Global Optimization with Polynomials and the Problem of Moments, SIAM Journal on Optimization, vol.11, issue.3, pp.796-817, 2001.
DOI : 10.1137/S1052623400366802

J. B. Lasserre and T. Priéto-rumeau, SDP vs. LP Relaxations for the Moment Approach in Some Performance Evaluation Problems, Stochastic Models, vol.17, issue.4, pp.439-456, 2004.
DOI : 10.1214/aos/1176325496

J. B. Lasserre, T. Priéto-rumeau, and M. Zervos, PRICING A CLASS OF EXOTIC OPTIONS VIA MOMENTS AND SDP RELAXATIONS, Mathematical Finance, vol.11, issue.1, pp.469-494, 2006.
DOI : 10.1287/moor.1040.0124

J. B. Lasserre, C. Prieur, and D. Henrion, Nonlinear optimal control: approximations via moments and LMI-relaxations, Proceedings of the 44th IEEE Conference on Decision and Control, pp.1648-1653, 2005.
DOI : 10.1109/CDC.2005.1582395

H. Maurer, On optimal control problems with bounded state variables and control appearing linearly, SIAM J. Cont. Optim, vol.15, pp.3-345, 1977.

J. Nash, The Imbedding Problem for Riemannian Manifolds, The Annals of Mathematics, vol.63, issue.1, pp.20-63, 1956.
DOI : 10.2307/1969989

H. J. Pesch, A practical guide to the solution of real-life optimal control problems, Control Cybernet, vol.23, pp.1-2, 1994.

C. Prieur and E. Trélat, Robust optimal stabilization of the Brockett integrator via a hybrid feedback, Mathematics of Control, Signals, and Systems, vol.17, issue.3, pp.201-216, 2005.
DOI : 10.1007/s00498-005-0152-9

URL : https://hal.archives-ouvertes.fr/hal-00086453

K. Schmüdgen, TheK-moment problem for compact semi-algebraic sets, Mathematische Annalen, vol.207, issue.1, pp.203-206, 1991.
DOI : 10.1007/BF01446568

M. 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

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 2002.

O. Von-stryk and R. Bulirsch, Direct and indirect methods for trajectory optimization, Annals of Operations Research, vol.9, issue.6, pp.357-373, 1992.
DOI : 10.1007/BF02071065

E. Trélat, Contrôle optimal: théorie et applications, 2005.

F. Vasilescu, Spectral measures and moment problems. Spectral Theory and Its Applications, pp.173-215, 2003.

R. Vinter, Convex Duality and Nonlinear Optimal Control, SIAM Journal on Control and Optimization, vol.31, issue.2, pp.518-538, 1993.
DOI : 10.1137/0331024