F. B. Argomedo, C. Prieur, E. Witrant, and S. Brémond, A strict control lyapunov function for a diffusion equation with time-varying distributed coefficients, IEEE Transactions on Automatic Control, p.2012, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00719502

M. Ariola and A. Pironti, Magnetic Control of Tokamak Plasmas Advances in Industrial Control, 2008.

A. Baaiu, F. Couenne, D. Eberard, C. Jallut, Y. Le-gorrec et al., Port-based modelling of mass transport phenomena, Mathematical and Computer Modelling of Dynamical Systems, vol.15, issue.3, pp.233-254, 2009.
DOI : 10.1080/13873950902808578

URL : https://hal.archives-ouvertes.fr/hal-00579370

A. Baaiu, F. Couenne, D. Eberard, C. Jallut, Y. Legorrec et al., Port-based modelling of mass transport phenomena, Mathematical and Computer Modelling of Dynamical Systems, vol.15, issue.3, pp.1-22, 2009.
DOI : 10.1080/13873950902808578

URL : https://hal.archives-ouvertes.fr/hal-00579370

A. Baaiu, F. Couenne, L. Lefevre, Y. L. Gorrec, and M. Tayakout-fayolle, Structure-preserving infinite dimensional model reduction: Application to adsorption processes, Journal of Process Control, vol.19, issue.3, pp.394-404, 2009.
DOI : 10.1016/j.jprocont.2008.07.002

URL : https://hal.archives-ouvertes.fr/hal-01625132

J. Blum, Numerical Simulation and Optimal Control in Plasma Physics, 1989.

A. H. Boozer, Onsager symmetry of transport in toroidal plasmas, Physics of Fluids B: Plasma Physics, vol.4, issue.9, pp.2845-2853, 1992.
DOI : 10.1063/1.861312

M. D. Boyer and E. Schuster, Adaptive nonlinear burn control in tokamak fusion reactors, 2012 American Control Conference (ACC), 2012.
DOI : 10.1109/ACC.2012.6315530

M. D. Boyer and E. Schuster, Nonlinear Burn Control in Tokamak Fusion Reactors via Output Feedback, 19th IFAC World Congress, 2014.
DOI : 10.3182/20140824-6-ZA-1003.01714

S. I. Braginskii, Reviews of Plasma Physics, 1965.

T. J. Courant, Dirac manifolds, Transactions of the American Mathematical Society, vol.319, issue.2, pp.631-661, 1990.
DOI : 10.1090/S0002-9947-1990-0998124-1

M. Dalsmo, A. J. Van, and . Schaft, On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems, SIAM Journal on Control and Optimization, vol.37, issue.1, pp.54-91, 1999.
DOI : 10.1137/S0363012996312039

S. R. De-groot and P. Mazur, Non-equilibrium thermodynamics. Dover Books on Physics, 1984.

A. Franco, P. Schott, C. Jallut, and B. M. Maschke, Multi-scale bond graph model of the electrochemical dynamics in a fuel cell, Proceedings of the of the 5th MathMod conference, 2006.

X. Garbet, Thermodynamics of neoclassical and turbulent transport, Plasma Physics and Controlled Fusion, vol.54, issue.5, 2012.
DOI : 10.1088/0741-3335/54/5/055007

O. Gaye, E. Moulay, S. Brémond, L. Autrique, R. Nouailletas et al., Sliding mode stabilization of the current profile in Tokamak plasmas, IEEE Conference on Decision and Control and European Control Conference, 2011.
DOI : 10.1109/CDC.2011.6160442

URL : https://hal.archives-ouvertes.fr/hal-00659093

G. Golo, V. Talasila, A. J. Van-der-schaft, and B. Maschke, Hamiltonian discretization of boundary control systems, Automatica, vol.40, issue.5, pp.757-771, 2004.
DOI : 10.1016/j.automatica.2003.12.017

B. Hamroun, L. Lefevre, and E. Mendes, Port-based modelling for open channel irrigation systems, Transactions on Fluid Mechanics, vol.1, issue.12, pp.995-1009, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00195129

B. Hamroun, L. Lefevre, and E. Mendes, A port-controlled hamiltonian approach to geometric reduction of distributed parameters systems -application to the shallow water equations, International Journal of Numerical Methods in Engineering, 2009.

D. C. Karnopp, D. L. Margolis, and R. C. Rosenberg, System Dynamics: Modeling and Simulation of Mechatronic Systems, 2006.
DOI : 10.1002/9781118152812

A. Kugi, Non-linear Control Based on Physical Models: Electrical, Hydraulic and Mechanical Systems, Lecture Notes in Control and Information Science, vol.260, 2000.

A. Macchelli and B. M. Maschke, Modeling and Control of Complex Physical Systems -The Port-Hamiltonian Approach, chapter Infinite-dimensional Port-Hamiltonian Systems, pp.211-272, 2009.

A. Macchelli and C. Melchiorri, Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach, SIAM Journal on Control and Optimization, vol.43, issue.2, pp.743-767, 2004.
DOI : 10.1137/S0363012903429530

J. E. Marsden and A. Weinstein, The Hamiltonian structure of the Maxwell-Vlasov equations, Physica D: Nonlinear Phenomena, vol.4, issue.3, pp.394-406, 1982.
DOI : 10.1016/0167-2789(82)90043-4

B. Maschke, A. J. Van, and . Schaft, Advanced Topics in Control Systems Theory. Lecture Notes from FAP, Lecture Notes on Control and Information Sciences, pp.115-154, 2004.

B. M. Maschke, A. J. Van, and . Schaft, Canonical interdomain coupling in distributed parameter systems: an extension of the symplectic gyrator, Proc. Int. Mechanical Engineering Congress and Exposition, 2001.

P. J. Morrison and J. M. Greene, Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics, Physical Review Letters, vol.12, issue.10, pp.790-794, 1980.
DOI : 10.1007/978-1-4757-1693-1

P. J. Morrison and J. M. Greene, Hamiltonian and action principle formulations of plasma physics, Physics of Plasmas, vol.10, issue.88, 2005.
DOI : 10.1063/1.1705885

G. Nishida and N. Sakamoto, Port-based modeling of magnetohydrodynamics equations for Tokamaks, 2010 IEEE International Conference on Control Applications, pp.842-847, 2010.
DOI : 10.1109/CCA.2010.5611289

G. Nishida, K. Takagi, and B. Maschke, Multiscale distributed porthamiltonian representation of ionic polymer-metal composite (ipmc), Proc. IFAC World Congress, pp.2300-2305, 2008.

G. Nishida, K. Takagi, B. Maschke, and T. Osada, Multi-scale distributed parameter modeling of ionic polymer-metal composite soft actuator, Control Engineering Practice, vol.19, issue.4, pp.321-334, 2011.
DOI : 10.1016/j.conengprac.2010.10.005

P. J. Olver, Applications of Lie Groups to Differential Equations, volume 107 of Graduate texts in mathematics, 1993.

L. Onsager, Reciprocal Relations in Irreversible Processes. I., Physical Review, vol.4, issue.4, p.2265, 1931.
DOI : 10.1002/andp.19103381612

Y. Ou, C. Xu, and E. Schuster, Robust control design for the poloidal magnetic flux profile evolution in the presence of model uncertainties, IEEE Transactions on Plasma Sciences, vol.32, issue.3, pp.375-382, 2010.

Y. Ou, C. Xu, E. Schuster, T. C. Luce, J. R. Ferron et al., Optimal Tracking Control of Current Profile in Tokamaks, IEEE Transactions on Control Systems Technology, vol.19, issue.2, pp.432-441, 2011.
DOI : 10.1109/TCST.2010.2046640

H. Ouarit, S. Brémond, R. Nouailletas, E. Witrant, and L. Autrique, Validation of plasma current profile model predictive control in tokamaks via simulations, Fusion Engineering and Design, vol.86, issue.6-8, 2010.
DOI : 10.1016/j.fusengdes.2011.03.078

A. Pironti and M. Walker, Fusion, tokamaks, and plasma control: an introduction and tutorial, IEEE Control Systems Magazine, vol.25, issue.5, pp.30-43, 2005.
DOI : 10.1109/MCS.2005.1512794

M. Polner, J. J. Van, and . Vegt, A Hamiltonian vorticity???dilatation formulation of the compressible Euler equations, Nonlinear Analysis: Theory, Methods & Applications, vol.109, issue.109, pp.113-135, 2014.
DOI : 10.1016/j.na.2014.07.005

A. Jamiolkowski and R. S. Ingarden, Classical Electrodynamics, 1985.

E. Schuster and M. Krstic, Control of a non-linear PDE system arising from non-burning tokamak plasma transport dynamics, International Journal of Control, vol.76, issue.11, pp.1116-1124, 2003.
DOI : 10.1109/TPS.1983.4316210

E. Schuster, M. Krstic, and G. Tynan, Nonlinear Lyapunov-based burn control in fusion reactors, Fusion Engineering and Design, vol.63, issue.64, pp.63-64569, 2002.
DOI : 10.1016/S0920-3796(02)00272-7

E. Schuster, M. Krstic, and G. Tynan, Burn Control in Fusion Reactors via Nonlinear Stabilization Techniques, Fusion Science and Technology, vol.26, issue.5, 2003.
DOI : 10.1088/0029-5515/41/3/308

S. Stramigioli, Modeling and IPC Control of Interactive Mechanical Systems: a Coordinate-free Approach, Lect. Notes in Control and Information Sci, vol.266, 2001.

E. Tassi, P. J. Morrison, F. L. Waelbroeck, and D. Grasso, Hamiltonian formulation and analysis of a collisionless fluid reconnection model, Plasma Physics and Controlled Fusion, vol.50, issue.8, p.50, 2008.
DOI : 10.1088/0741-3335/50/8/085014

A. J. Van and . Schaft, L 2 -Gain and Passivity Techniques in Nonlinear Control Springer Communications and Control Engineering series, Notes in Control and Inf. Sciences, 1996.

A. J. Van-der-schaft and B. M. Maschke, The Hamiltonian formulation of energy conserving physical systems with external ports. Archiv für Elektronik und¨Ubertragungstechnikund¨ und¨Ubertragungstechnik, pp.362-371, 1995.

A. J. Van-der-schaft and B. M. Maschke, Hamiltonian formulation of distributed-parameter systems with boundary energy flow, Journal of Geometry and Physics, vol.42, issue.1-2, pp.166-174, 2002.
DOI : 10.1016/S0393-0440(01)00083-3

V. Duindam, A. Macchelli, S. Stramigioli, and H. , Modeling and Control of Complex Physical Systems -The Port-Hamiltonian Approach, 2009.

T. N. Vu, L. Lefèvre, R. Nouailletas, and S. Brémond, Geometric discretization for a plasma control model, IFAC Joint conference: 5th Symposium on System Structure and Control, 2013.
DOI : 10.3182/20130204-3-FR-2033.00098

T. N. Vu, L. Lefèvre, R. Nouailletas, and S. Brémond, Structure preserving reduction for thermo-magneto plasma control model, The 21st International Symposium on Mathematical Theory of Networks and Systems, 2014.

M. L. Walker, D. A. Humphreys, D. Mazon, D. Moreau, M. Okabayashi et al., Emerging applications in tokamak plasma control, IEEE Control Systems Magazine, vol.26, issue.2, pp.35-63, 2006.
DOI : 10.1109/MCS.2006.1615272

E. Witrant, E. Joffrin, S. Brémond, G. Giruzzi, D. Mazon et al., A control-oriented model of the current profile in tokamak plasma, Plasma Physics and Controlled Fusion, vol.49, issue.7, pp.1075-1105, 2007.
DOI : 10.1088/0741-3335/49/7/009

URL : https://hal.archives-ouvertes.fr/hal-00387534