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, 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

G. Besançon, J. F. Dulhoste, and D. Georges, A nonlinear backstepping like controller for a three-point collocation model of water flow dynamics, Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01) (Cat. No.01CH37204), 2001.
DOI : 10.1109/CCA.2001.973860

G. Blankenstein and T. S. Ratiu, Singular reduction of implicit Hamiltonian systems, Reports on Mathematical Physics, vol.53, issue.2, pp.211-260, 2004.
DOI : 10.1016/S0034-4877(04)90013-4

G. Blankenstein, A. J. Van, and . Schaft, Symmetry and reduction in implicit generalized Hamiltonian systems, Reports on Mathematical Physics, vol.47, issue.1, pp.57-100, 2001.
DOI : 10.1016/S0034-4877(01)90006-0

A. Bossavit, Differential forms and the computation of fields and forces in electromagnetism, European Journal of Mechanics, B/Fluids, vol.10, issue.5, pp.474-488, 1991.

A. Bossavit, Computational Electromagnetism, 1998.

J. Cervera, A. J. Van-der-schaft, and A. Baños, Interconnection of port-Hamiltonian systems and composition of Dirac structures, Automatica, vol.43, issue.2, pp.212-225, 2007.
DOI : 10.1016/j.automatica.2006.08.014

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

T. J. Courant and A. Weinstein, Beyond Poisson structures, Séminaire Sud-Rhodanien de Géométrie, 1988.

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

A. Barré-de-saint-venant, Théorie du mouvement non-permanent des eaux avec application aux crues des rivières et à introduction des marées dans leur lit, Comptes rendus de l'Académie des Sciences, pp.148-154, 1871.

I. Ya and . Dorfman, Dirac structure of integrable evolution equations, Physics Letters A, vol.125, pp.240-246, 1987.

I. Ya and . Dorfman, Dirac structures and integrability of nonlinear evolution equations, 1993.

J. F. Dulhoste, G. Besançon, and D. Georges, Nonlinear control of water flow dynamics by input-output linearization based on collocation model, Proceedings of the European Control Conference ECC, 2001.

B. Fornberg, A Practical Guide to Pseudospectral Methods, 1996.
DOI : 10.1017/CBO9780511626357

A. Franco, P. Schott, C. Jallut, and B. M. Maschke, A Multi-Scale Dynamic Mechanistic Model for the Transient Analysis of PEFCs, Fuel Cells, vol.150, issue.2, pp.99-117, 2007.
DOI : 10.1002/fuce.200500204

A. J. Van-der-schaft, G. Golo, V. Talasila, and B. Maschke, Hamiltonian discretization of the the Telegrapher's equation, Automatica, 2004.

G. Golo, Interconnection Structures in Port-Based Modelling: Tools for Analysis and Simulation, 2002.

W. H. Graf and M. S. Altinakar, Hydraulique fluviale -Ecoulement et phénomènes de transport dans les canaux à géométrie simple, volume 16 of Traité de génie civil de l'Ecole Polytechnique Fédérale de Lausanne, Presses Polytechniques Universitaires Romandes, 2000.

H. 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

H. Hamroun, L. Lefevre, and E. Mendes, Port-based modelling for open channel irrigation systems, Proceedings of the 2nd IASME/WSEAS Int.ernational Conference on Water Resources, Hydraulics and Hydrology, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00195129

F. M. Lasagni, Canonical Runge-Kutta methods, ZAMP Zeitschrift f???r angewandte Mathematik und Physik, vol.4, issue.6, pp.952-953, 1988.
DOI : 10.1007/BF00945133

Y. , L. Gorrec, H. Zwart, and B. M. Maschke, Dirac structures and boundary control systems associated with skew-symmetric differential operators

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

B. Maschke, A. J. Van, and . Schaft, Advanced Topics in Control Systems Theory. Lecture Notes from FAP 2004, chapter Compositional modelling of distributed-parameter systems, Lecture Notes on Control and Information Sciences, pp.115-154, 2005.

B. M. Maschke, R. Ortega, A. J. Van, and . Schaft, Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation, IEEE Trans. on Automatic Control, issue.8, pp.451498-1502, 2000.

B. M. Maschke, A. J. Van, and . Schaft, Canonical interdomain coupling in distributed parameter systems: an extension of the symplectic gyrator

B. M. Maschke, A. J. Van, and . Schaft, Modelling and Control of Mechanical Systems, chapter Interconnected Mechanical systems, pp.1-30, 1997.

B. M. Maschke, A. J. Van-der-schaft, and P. C. Breedveld, An intrinsic hamiltonian formulation of network dynamics: non-standard poisson structures and gyrators, Journal of the Franklin Institute, vol.329, issue.5, pp.923-966, 1992.
DOI : 10.1016/S0016-0032(92)90049-M

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

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

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

R. Ortega, A. Van-der-schaft, F. Castanos, and A. Astolfi, Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems, IEEE Transactions on Automatic Control, vol.53, issue.11, p.53, 2008.
DOI : 10.1109/TAC.2008.2006930

R. Ortega, A. J. Van-der-schaft, B. Maschke, and G. Escobar, Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems, Automatica, vol.38, issue.4, pp.585-596, 2002.
DOI : 10.1016/S0005-1098(01)00278-3

H. Ouarit, D. Lefèvre, and . Georges, Robust optimal control of onereach open-channels, Proc. European Control Conference ECC'2003, 2003.

A. Parsian, A. Shafei-deh, and . Abad, Dirac structures on Hilbert spaces, International Journal of Mathematics and Mathematical Sciences, vol.22, issue.1, pp.97-108, 1999.
DOI : 10.1155/S0161171299220972

S. Reich, Multi-Symplectic Runge???Kutta Collocation Methods for Hamiltonian Wave Equations, Journal of Computational Physics, vol.157, issue.2, pp.473-499, 2000.
DOI : 10.1006/jcph.1999.6372

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

J. M. Sanz-serna, Runge-kutta schemes for Hamiltonian systems, BIT, vol.6, issue.4, pp.877-883, 1988.
DOI : 10.1007/978-1-4757-1693-1

C. Valentin, M. Magos, and B. Maschke, A port-Hamiltonian formulation of physical switching systems with varying constraints, Automatica, vol.43, issue.7, pp.1125-1133, 2007.
DOI : 10.1016/j.automatica.2006.12.022

A. J. Van and . Schaft, Implicit hamiltonian systems with symmetry, Reports on Mathematical Physics, vol.41, pp.203-221, 1994.

A. J. Van-der-schaft and B. M. Maschke, On the Hamiltonian formulation of nonholonomic mechanical systems, Reports on Mathematical Physics, vol.34, issue.2, pp.225-233, 1994.
DOI : 10.1016/0034-4877(94)90038-8

A. J. Van-der-schaft and B. M. Maschke, The Hamiltonian formulation of energy conserving physical systems with external ports, Archiv für Elektronik und Übertragungstechnik, 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

A. J. Van-der-schaft and B. M. Maschke, Model Based Control: bridging rigorous theory and advanced technology, chapter Conservation laws and lumped system dynamics, pp.31-48, 2009.

H. Yoshimura and J. E. Marsden, Dirac structures in Lagrangian mechanics Part I: Implicit Lagrangian systems, Journal of Geometry and Physics, vol.57, issue.1, pp.133-156, 2006.
DOI : 10.1016/j.geomphys.2006.02.009