H. Grad and J. Hogan, Classical Diffusion in a Tokomak, Physical Review Letters, vol.24, issue.24, pp.1337-1340, 1970.
DOI : 10.1103/PhysRevLett.24.1337

H. Grad and H. Rubin, Hydromagnetic equilibria and force-free fields, Journal of Nuclear Energy (1954), vol.7, issue.3-4, pp.190-197, 1958.
DOI : 10.1016/0891-3919(58)90139-6

V. Shafranov, On magnetohydrodynamical equilibrium configurations, Soviet Physics JETP, vol.6, issue.3, p.1013, 1958.

C. Mercier, The MHD approach to the problem of plasma confinement in closed magnetic configurations, Lectures in Plasma Physics, Commission of the European Communities, 1974.

L. Lao, J. Ferron, R. Geoebner, W. Howl, H. St et al., Equilibrium analysis of current profiles in tokamaks, Nuclear Fusion, vol.30, issue.6, p.1035, 1990.
DOI : 10.1088/0029-5515/30/6/006

J. Blum, E. Lazzaro, J. O-'rourke, B. Keegan, and Y. Stefan, Problems and methods of self-consistent reconstruction of tokamak equilibrium profiles from magnetic and polarimetric measurements, Nuclear Fusion, vol.30, issue.8, p.1475, 1990.
DOI : 10.1088/0029-5515/30/8/007

J. Blum and H. Buvat, An inverse problem in plasma physics : The identification of the current density profile in a tokamak Large Scale Optimization with applications, Part 1: Optimization in inverse problems and design, IMA Volumes in Mathematics and its Applications, pp.17-36, 1997.

V. D. Shafranov, in a Tokamak for arbitrary shape of plasma pinch cross-section, Plasma Physics, vol.13, issue.9, p.757, 1971.
DOI : 10.1088/0032-1028/13/9/006

L. Zakharov and V. Shafranov, Equilibrium of a toroidal plasma with noncircular cross-section, Sov. Phys, Tech. Phys, vol.18, issue.2, pp.151-156, 1973.

J. Luxon and B. Brown, Magnetic analysis of non-circular cross-section tokamaks, Nuclear Fusion, vol.22, issue.6, pp.813-821, 1982.
DOI : 10.1088/0029-5515/22/6/009

D. Swain and G. Neilson, An efficient technique for magnetic analysis of non-circular, high-beta tokamak equilibria, Nuclear Fusion, vol.22, issue.8, pp.1015-1030, 1982.
DOI : 10.1088/0029-5515/22/8/002

L. Lao, in tokamaks of non-circular cross-section, Nuclear Fusion, vol.25, issue.10, p.1421, 1985.
DOI : 10.1088/0029-5515/25/10/004

J. Blum, Numerical Simulation and Optimal Control in Plasma Physics with Applications to Tokamaks, Series in Modern Applied Mathematics, 1989.

F. Hofmann and G. Tonetti, Tokamak equilibrium reconstruction using Faraday rotation measurements, Nuclear Fusion, vol.28, issue.10, p.1871, 1988.
DOI : 10.1088/0029-5515/28/10/014

URL : http://infoscience.epfl.ch/record/120899

J. Christiansen and J. Taylor, Determination of current distribution in a tokamak, Nuclear Fusion, vol.22, issue.1, 1982.
DOI : 10.1088/0029-5515/22/1/011

B. Braams, The interpretation of tokamak magnetic diagnostics, Plasma Physics and Controlled Fusion, vol.33, issue.7, p.715, 1991.
DOI : 10.1088/0741-3335/33/7/001

M. Bishop and J. Taylor, Degenerate toroidal MHD equilibria and minimum B, Physics of fluids, vol.29, p.1444, 1986.
DOI : 10.1063/1.865913

V. Pustovitov, Magnetic diagnostics: General principles and the problem of reconstruction of plasma current and pressure profiles in toroidal systems, Nuclear Fusion, vol.41, issue.6, p.721, 2001.
DOI : 10.1088/0029-5515/41/6/307

L. Zakharov, J. Lewandoski, E. Foley, F. Levinton, H. Yuh et al., The theory of variances in equilibrium reconstruction, Physics of Plasmas, vol.15, issue.9, p.92503, 2008.
DOI : 10.1063/1.2977480

W. Zwingmann, L. Eriksson, and P. Stubberfield, Equilibrium analysis of tokamak discharges with anisotropic pressure, Plasma Physics and Controlled Fusion, vol.43, issue.11, pp.1441-1456, 2001.
DOI : 10.1088/0741-3335/43/11/302

M. Beretta and M. Vogelius, An inverse problem originating from magnetohydrodynamics, Archive for Rational Mechanics and Analysis, vol.43, issue.2, pp.137-152, 1991.
DOI : 10.1007/BF00375223

M. Beretta and M. Vogelius, An inverse problem originating from magnetohydrodynamics III. domains with corners of arbitrary angles, Asymptotic Analysis, vol.11, pp.289-315, 1992.

M. Vogelius, An inverse problem for the equation ?u = ?cu?d, pp.1181-1209, 1994.

A. Demidov, A. Y. Kochurov, and A. S. Popov, To the problem of the recovery of nonlinearities in equations of mathematical physics, Journal of Mathematical Sciences, vol.44, issue.6, pp.46-77, 2009.
DOI : 10.1007/s10958-009-9658-x

M. Beretta and M. Vogelius, An inverse problem originating from magnetohydrodynamics II. the case of the Grad-Shafranov equation, Indiana Univ, Math. J, pp.41-1081, 1992.

D. O. 'brien, J. Ellis, and J. Lingertat, Local expansion method for fast plasma boundary identification in JET, Nuclear Fusion, vol.33, issue.3, pp.467-474, 1993.
DOI : 10.1088/0029-5515/33/3/I08

F. Saint-laurent and G. Martin, Real time determination and control of the plasma localisation and internal inductance in Tore Supra, Fusion Engineering and Design, vol.56, issue.57, pp.56-57, 2001.
DOI : 10.1016/S0920-3796(01)00399-4

F. Sartori, A. Cenedese, and F. Milani, JET real-time object-oriented code for plasma boundary reconstruction, Fusion Engineering and Design, vol.66, issue.68, pp.66-68, 2003.
DOI : 10.1016/S0920-3796(03)00290-4

A. Tikhonov and V. Arsenin, Solutions of Ill-posed problems, 1977.

P. Ciarlet, The Finite Element Method For Elliptic Problems, 1980.

C. and D. Boor, A Practical Guide To Splines, 1978.

P. Hansen, REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems, Numerical Algorithms, vol.55, issue.Suppl., pp.195-196, 1999.
DOI : 10.1007/BF02149761

D. Mazon, J. Blum, C. Boulbe, B. Faugeras, A. Boboc et al., Real-time identification of the current density profile in the JET tokamak: method and validation, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, pp.285-290, 2009.
DOI : 10.1109/CDC.2009.5399695

URL : https://hal.archives-ouvertes.fr/hal-00414481

D. Mazon, J. Blum, C. Boulbe, B. Faugeras, A. Boboc et al., EQUINOX: A REAL-TIME EQUILIBRIUM CODE AND ITS VALIDATION AT JET, From physics to control through an emergent view of World Scientific Book Series On Nonlinear Science, Series B, World Scientific, pp.327-333, 2010.
DOI : 10.1142/9789814313155_0050

URL : https://hal.archives-ouvertes.fr/hal-00872242