D. Pham-van-thang, G. Georges, and . Besançon, Infinite-dimensional Receding Horizon Optimal Control for an Open-channel System, Proceedings of 8th IFAC Symposium on Nonlinear Control Systems, 2010.

D. Pham-van-thang, G. Georges, and . Besançon, On the Use of a Global Control Lyapunov Functional in Infinite-dimensional Predictive Control, Proceedings of 4th IFAC Symposium on System, Structure and Control, 2010.

D. Pham-van-thang, G. Georges, and . Besançon, Predictive Control with guaranteed stability for hyperbolic systems of conservation laws, Proceeding of 49th IEEE Conference on Decision and Control, 2010.

D. Pham-van-thang, G. Georges, and . Besançon, Receding Optimal Boundary Control of Non-linear Hyperbolic Systems of Conservation Laws, in 'Proceeding of 18th World Congress of the International Federation of Automatic Control, RHOC for linearized Saint-Venant equations 2010c], [Pham, p.and, 2011.

B. Chopard and M. Droz, Cellular Automata Modeling of Physical Systems, 2005.

J. M. Coron, B. Novel, and G. Bastin, A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws, IEEE Transactions on Automatic Control, vol.52, issue.1, pp.2-11, 2007.
DOI : 10.1109/TAC.2006.887903

R. F. Curtain and H. J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, 1995.
DOI : 10.1007/978-1-4612-4224-6

R. Findensen and F. Allgower, An introduction to nonlinear model predictive control, 21st Benelux Meeting on Systems and Control, 2002.

D. Georges, Infinite-dimensional nonlinear predictive control design for open-channel hydraulic systems. Networks and Heterogeneous Media, pp.1-18, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00384966

K. Ito and K. Funisch, Receding horizon optimal control for infinite dimensional systems. ESAIM: Control, Optimisation and Calculus of Variations, pp.741-760, 2002.

M. Junk and M. Rheinlainder, Regular and multiscale expansions of a lattice Boltzmann method, Progress in Computational Fluid Dynamics, 2008.
DOI : 10.1504/PCFD.2008.018076

D. Q. Mayne and H. Michalska, Receding horizon control of nonlinear systems, IEEE Transactions on Automatic Control, vol.35, issue.7, pp.814-824, 1990.
DOI : 10.1109/9.57020

V. T. Pham, B. Chopard, L. Lefèvre, D. A. Ondo, and E. Mendes, Study of the 1d lattice boltzmann shallow water equation and its coupling to build a canal network, Journal of Computational Physics, vol.229, pp.7373-7400, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00580905

U. M. Ascher, R. Mattheij, and R. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, 1995.
DOI : 10.1137/1.9781611971231

G. Bastin and J. M. Coron, Further results on boundary feedback stabilisation of 2x2 hyperbolic systems over a bounded interval, 8th IFAC Symposium on Nonlinear Control Systems, 2010.

G. Bastin, J. M. Coron, and B. D. , Andréa-Novel, On the Lyapunov stability of linearised Saint-Venant equations for a slopping channel, Network and Heterogeneous Media, pp.177-187, 2009.

M. A. Cirina, Boundary Controllability of Nonlinear Hyperbolic Systems, SIAM Journal on Control, vol.7, issue.2, pp.198-212, 1969.
DOI : 10.1137/0307014

J. M. Coron, B. D-'andréa-novel, and G. Bastin, A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws, IEEE Transactions on Automatic Control, vol.52, issue.1, pp.52-54, 2007.
DOI : 10.1109/TAC.2006.887903

R. F. Curtain and H. J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, 1995.
DOI : 10.1007/978-1-4612-4224-6

R. F. Curtain, Linear-quadratic control problem with fixed endpoints in infinite dimensions, Journal of Optimization Theory and Applications, vol.16, issue.1, pp.55-74, 1984.
DOI : 10.1007/BF00934894

R. Findeisen and F. Allgöwer, An introduction to nonlinear model predictive control, 21st Benelux Meeting on Systems and Control, 2002.

R. Findeisen, L. Imsland, F. Allgöwer, and B. A. Foss, State and Output Feedback Nonlinear Model Predictive Control: An Overview, European Journal of Control, vol.9, issue.2-3, pp.179-195, 2003.
DOI : 10.3166/ejc.9.190-206

D. Georges, Infinite-dimensional nonlinear predictive control design for open-channel hydraulic systems, Networks and Heterogeneous Media, pp.1-18, 2009.

W. H. Graf and M. S. Altinakar, Hydraulique fluviale -´ Ecoulement et phénomènes de transport dans les canauxàcanaux`canauxà géométrie simple, 2000.

K. Ito and K. Kunisch, Receding horizon optimal control for infinite dimensional systems, ESAIM: Control, Optimisation and Calculus of Variations, pp.741-760, 2002.

I. Lasiecka and R. Triggiani, Control Theory for Partial Diffrential Equations: Continuous and Approximation Theories Volume II Abstract Hyperbolic-like Systems over a Finite Time Horizon, 2000.

T. Li and B. Rao, Exact boundary controllability of unsteady flows in a tree-like network of open canals, Methods and Applications of Analysis, pp.353-366, 2004.

T. T. Li, B. Rao, and Y. Lin, Semi-global C1 solution and exact boundary controllability for reducible quasilinear hyperbolic systems, Modélisation mathématique et analyse numérique, pp.399-408, 2000.

X. Litrico and V. Fromion, Boundary control of hyperbolic conservation laws using a frequency domain approach, Automatica, 2009.

D. G. Luenberger, Optimization by Vector Space Methods, 1969.

D. Q. Mayne and H. Michalska, Receding horizon control of nonlinear systems, IEEE Transactions on Automatic Control, pp.35-814, 1990.

V. T. Pham, D. Georges, and G. Besançon, Infinite-dimensional receding horizon optimal control for an open-channel system On the use of a global control lyapunov functional in infinite-dimensional predictive control, 8th IFAC Symposium on Nonlinear Control Systems 4th IFAC Symposium on System, Structure and Control Predictive control with guaranteed stability for hyperbolic systems of conservation laws 49th IEEE Conference on Decision and Control, 2010.

J. Rauch, L2 is a continuable initial condition for kreiss' mixed problems, Communications on Pure and Applied Mathematics, vol.10, issue.3, pp.265-285, 1972.
DOI : 10.1002/cpa.3160250305

J. Rauch and M. Taylor, Exponential Decay of Solutions to Hyperbolic Equations in Bounded Domains, Indiana University Mathematics Journal, vol.24, issue.1, pp.79-86, 1974.
DOI : 10.1512/iumj.1975.24.24004

J. B. Rauch and F. J. Massey, Differentiability of solution to hyperbolic initial boundary value problems, Transactions of the, pp.303-318, 1974.

D. L. Russell, Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions, SIAM Review, vol.20, issue.4, pp.639-739, 1978.
DOI : 10.1137/1020095

R. Szymkiewicz, Numerical modeling in Open Channel Hydraulics, Water Science and Technology Library, vol.83, 2010.
DOI : 10.1007/978-90-481-3674-2

C. Z. Xu and G. Sallet, Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems, ESAIM: Control, Optimization and Calculus of Variations, pp.421-442, 2002.

R. Bastin, G. Haut, B. Coron, J. M. Andréa-novel, and B. , Lyapunov stability analysis of networks of scalar conservation laws, Networks and Heterogeneous Media, pp.749-757, 2007.
DOI : 10.3934/nhm.2007.2.751

S. Boyd and L. A. Vandenberghe, Convex optimization Hyperbolic systems of conservation laws ? the one-dimensional cauchy problem, 2000.

R. M. Colombo and P. Goatin, A well posed conservation law with a variable unilateral constraint, Journal of Differential Equations, vol.234, issue.2, pp.654-675, 2007.
DOI : 10.1016/j.jde.2006.10.014

R. M. Colombo, P. Goatin, and M. D. Rosini, On the modelling and management of traffic, ESAIM: Mathematical Modelling and Numerical Analysis, vol.45, issue.5, pp.853-872, 2011.
DOI : 10.1051/m2an/2010105

S. Dubljevic, P. Mhaskar, P. D. Christofides, and N. H. El-farra, Predictive control of transport-reaction processes, Computers & Chemical Engineering, vol.29, issue.11-12, pp.11-2335, 2005.
DOI : 10.1016/j.compchemeng.2005.05.008

R. Findeisen, L. Imsland, F. Allgöwer, and B. A. Foss, State and Output Feedback Nonlinear Model Predictive Control: An Overview, European Journal of Control, vol.9, issue.2-3, pp.179-195, 2003.
DOI : 10.3166/ejc.9.190-206

D. Georges, Infinite-dimensional nonlinear predictive control design for open-channel hydraulic systems. Networks and Heterogeneous Media, pp.1-18, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00384966

D. Georges and X. Litrico, Automatique pour la gestion des ressources en eau, 2002.

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, 1995.
DOI : 10.1137/1037043

K. Ito and K. Kunisch, Receding horizon optimal control for infinite dimensional systems. ESAIM: Control, Optimisation and Calculus of Variations, pp.741-760, 2002.
DOI : 10.1051/cocv:2002032

URL : http://archive.numdam.org/article/COCV_2002__8__741_0.pdf

L. Mohammadi, S. Dubljevic, and J. F. Forbes, Robust characteristic-based MPC of a fixed-bed reactor, Proceedings of the 2010 American Control Conference, 2010.
DOI : 10.1109/ACC.2010.5531050

V. T. Pham, D. Georges, and G. Besançon, Predictive Control with guaranteed stability for hyperbolic systems of conservation laws, 49th IEEE Conference on Decision and Control (CDC), 2010.
DOI : 10.1109/CDC.2010.5718009

URL : https://hal.archives-ouvertes.fr/hal-00551283

D. Serre, Systems of Conservation law 1: Hyperbolicity, entropies, shock waves, 1999.
DOI : 10.1017/CBO9780511612374

H. Shang, J. F. Forbes, and M. Guay, Model Predictive Control for Quasilinear Hyperbolic Distributed Parameter Systems, Industrial & Engineering Chemistry Research, vol.43, issue.9, pp.2140-2149, 2004.
DOI : 10.1021/ie030653z

H. Shang, J. F. Forbes, and M. Guay, Feedback control of hyperbolic distributed parameter systems, Chemical Engineering Science, vol.60, issue.4, pp.969-980, 2005.
DOI : 10.1016/j.ces.2004.09.067

H. Shang, J. F. Forbes, and M. Guay, Computationally efficient model predictive control for convection dominated parabolic systems, Journal of Process Control, vol.17, issue.4, pp.379-386, 2007.
DOI : 10.1016/j.jprocont.2006.09.009

I. Aksikas, J. J. Winkin, and D. Dochain, Asymptotic stability of infinite-dimensional semilinear systems: Application to a nonisothermal reactor, Systems & Control Letters, vol.56, issue.2, pp.122-132, 2007.
DOI : 10.1016/j.sysconle.2006.08.012

S. Boyd and L. Vandenberghe, Convex Optimization, 2004.

B. Chopard and M. Droz, Cellular Automata Modeling of Physical Systems, 2005.

J. M. Coron, B. D-'andréa-novel, and G. Bastin, A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws, IEEE Transactions on Automatic Control, vol.52, issue.1, pp.2-11, 2007.
DOI : 10.1109/TAC.2006.887903

R. F. Curtain and H. J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, 1995.
DOI : 10.1007/978-1-4612-4224-6

M. Dick, M. Gugat, and G. Leugering, Classical solutions and feedback stabilization for the gas flow in a sequence of pipes. Networks and Heterogeneous Media, pp.691-709, 2010.

R. Findeisen, L. Imsland, F. Allgöwer, and B. A. Foss, State and Output Feedback Nonlinear Model Predictive Control: An Overview, European Journal of Control, vol.9, issue.2-3, pp.179-195, 2003.
DOI : 10.3166/ejc.9.190-206

D. Georges, Infinite-dimensional nonlinear predictive control design for open-channel hydraulic systems. Networks and Heterogeneous Media, pp.1-18, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00384966

A. Haraux, Recent results on semi-linear hyperbolic problems in bounded domains, Partial Differential Equations, vol.73, issue.4, pp.118-126, 1988.
DOI : 10.1017/S002776300001833X

A. Haraux and E. Zuazua, Decay estimates for some semilinear damped hyperbolic problems. Archive for Rational Mechanics and Analysis, pp.191-206, 1987.

K. Ito and K. Kunisch, Receding horizon optimal control for infinite dimensional systems. ESAIM: Control, Optimisation and Calculus of Variations, pp.741-760, 2002.

M. Junk and M. Rheinlainder, Regular and multiscale expansions of a lattice Boltzmann method, Progress in Computational Fluid Dynamics, 2008.
DOI : 10.1504/PCFD.2008.018076

B. E. Larock, R. W. Jeppson, and G. Z. Watters, Hydraulics of Pipeline Systems, 2000.
DOI : 10.1201/9781420050318

J. Liu, D. M. Pe-na, P. D. Christofides, and J. F. Davis, Lyapunov-based model predictive control of nonlinear systems subject to time-varying measurement delays, International Journal of Adaptive Control and Signal Processing, vol.39, issue.9, pp.788-807, 2009.
DOI : 10.1002/acs.1085

D. G. Luenberger, Optimization by Vector Space Methods, 1969.

Z. Luo, B. Guo, and O. Morgül, Stability and Stabilization of Infinite Dimensional Systems with Applications, 1999.
DOI : 10.1007/978-1-4471-0419-3

D. Q. Mayne and H. Michalska, Receding horizon control of nonlinear systems, IEEE Transactions on Automatic Control, vol.35, issue.7, pp.814-824, 1990.
DOI : 10.1109/9.57020

P. Mhaskar, N. H. El-farra, and P. D. Christofides, Predictive control of switched nonlinear systems with scheduled mode transitions, IEEE Transactions on Automatic Control, vol.50, issue.11, pp.1670-1680, 2005.
DOI : 10.1109/TAC.2005.858692

S. Oharu and T. Takahashi, On semigroup generated by m-accrerive operators in a strict sense, Proceedings of the American mathematical society, 1986.

S. Oharu and T. Takahashi, Locally Lipschitz continuous perturbations of linear dissipative operators and nonlinear semigroups, Proceedings of the American mathematical society, 1987.
DOI : 10.1090/S0002-9939-1987-0883426-5

A. Pazy, Semigroups of linear operators and Application to Partial Differential Equations, Applied Mathematical Sciences, vol.44, 1983.
DOI : 10.1007/978-1-4612-5561-1

V. T. Pham, D. Georges, and G. Besançon, Infinite-dimensional Receding Horizon Optimal Control for an Open-channel System, Proceedings of 8th IFAC Symposium on Nonlinear Control Systems, 2010.
DOI : 10.3182/20100901-3-IT-2016.00216

URL : https://hal.archives-ouvertes.fr/hal-00551277

V. T. Pham, D. Georges, and G. Besançon, Predictive Control with guaranteed stability for hyperbolic systems of conservation laws, 49th IEEE Conference on Decision and Control (CDC), 2010.
DOI : 10.1109/CDC.2010.5718009

URL : https://hal.archives-ouvertes.fr/hal-00551283

C. Prieur, Control of systems of conservation laws with boundary errors. Networks and Heterogeneous Media, pp.393-407, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00392197

E. Schechter, Evolution generated by semilinear dissipative plus compact operators. Transactions of the, pp.297-308, 1983.

J. Yong, Existence theory of optimal controls for distributed parameter systems, Kodai Mathematical Journal, vol.15, issue.2, pp.193-220, 1992.
DOI : 10.2996/kmj/1138039597

I. Draft-bibliography-aksikas, A. Fuxmana, J. F. Forbes, and J. J. Winkin, LQ control design of a class of hyperbolic PDE systems: Application to fixed-bed reactor, Automatica, vol.45, issue.6, pp.1542-1548, 2009.
DOI : 10.1016/j.automatica.2009.02.017

I. Aksikas, J. J. Winkin, and D. Dochain, Asymptotic stability of infinite-dimensional semilinear systems: Application to a nonisothermal reactor, Systems & Control Letters, vol.56, issue.2, pp.122-132, 2007.
DOI : 10.1016/j.sysconle.2006.08.012

I. Aksikas, J. J. Winkin, and D. Dochain, Optimal LQ-Feedback Regulation of a Nonisothermal Plug Flow Reactor Model by Spectral Factorization, IEEE Transactions on Automatic Control, vol.52, issue.7, pp.1179-1193, 2007.
DOI : 10.1109/TAC.2007.900823

M. Alamir, Optimization based non-linear observers revisited, International Journal of Control, vol.72, issue.13, pp.1204-1217, 1999.
DOI : 10.1080/002071799220353

U. Ascher, R. Matthe?, and R. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, 1995.
DOI : 10.1137/1.9781611971231

B. Bamieh, F. Paganini, and M. A. Dahleh, Distributed control of spatially invariant systems, IEEE Transactions on Automatic Control, vol.47, issue.7, pp.1091-1107, 2012.
DOI : 10.1109/TAC.2002.800646

G. Bastin and J. Coron, Further results on boundary feedback stabilisation of 2 ?? 2 hyperbolic systems over a bounded interval, Proceedings of 8th IFAC Symposium on Nonlinear Control Systems, 2010.
DOI : 10.3182/20100901-3-IT-2016.00167

G. Bastin, B. Haut, J. Coron, and B. Andréa-novel, Lyapunov stability analysis of networks of scalar conservation laws, Networks and Heterogeneous Media, pp.749-757, 2007.
DOI : 10.3934/nhm.2007.2.751

A. M. Bayen, R. L. Raffard, and C. J. Tomlin, Adjoint-based control of a new eulerian network model of air traffic flow, IEEE Transactions on Control Systems Technology, vol.14, issue.5, pp.804-818, 2006.
DOI : 10.1109/TCST.2006.876904

A. Bibliography-bressan, Hyperbolic Systems of Conservation Laws -The One-dimensional Cauchy Problem, 2000.

J. M. Burgers, A mathematical model illustrating the theory of turbulence', Advances in Applied Mechanics 1, pp.171-199, 1948.

H. Chen and F. Allgöwer, A Quasi-Infinite Horizon Nonlinear Model Predictive Control Scheme with Guaranteed Stability??????This paper was not presented at any IFAC meeting. This paper was accepted for publication in revised form by Associate Editor W. Bequette under the direction of Editor Prof. S. Skogestad., Automatica, vol.34, issue.10, pp.1205-1217, 1998.
DOI : 10.1016/S0005-1098(98)00073-9

M. L. Chen and D. Georges, Nonlinear optimal control of an open-channel hydraulic system based on an infinite-dimensional model, Proceedings of the 38th Conference on Decision & Control, 1999.

B. Chopard and M. Droz, Cellular Automata Modeling of Physical Systems, 2005.

P. D. Christofides and P. Daoutidis, Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds, Proceedings of the 36th IEEE Conference on Decision and Control, pp.398-420, 1997.
DOI : 10.1109/CDC.1997.657588

P. D. Christofides and P. Daoutidis, Robust control of hyperbolic PDE systems, Chemical Engineering Science, vol.53, issue.1, pp.85-105, 1998.
DOI : 10.1016/S0009-2509(97)87571-9

M. A. Cirina, Boundary Controllability of Nonlinear Hyperbolic Systems, SIAM Journal on Control, vol.7, issue.2, pp.198-212, 1969.
DOI : 10.1137/0307014

R. Colombo and P. Goatin, A well posed conservation law with a variable unilateral constraint, Journal of Differential Equations, vol.234, issue.2, pp.654-675, 2007.
DOI : 10.1016/j.jde.2006.10.014

R. M. Colombo, P. Goatin, and M. D. Rosini, On the modelling and management of traffic, ESAIM: Mathematical Modelling and Numerical Analysis, vol.45, issue.5, pp.853-872, 2011.
DOI : 10.1051/m2an/2010105

J. Coron, G. Bastin, and B. Andréa-novel, On Lyapunov stability of linearised Saint-Venant equations for a sloping channel, Networks and Heterogeneous Media, 2009.

J. Coron, B. D-'andréa-novel, and G. Bastin, A Lyapunov approach to control irrigation canals modeled by saint-venant equations, Proceedings of European Control Conference, 1999.

J. Coron, B. D-'andréa-novel, and G. Bastin, A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws, IEEE Transactions on Automatic Control, vol.52, issue.1, pp.2-11, 2007.
DOI : 10.1109/TAC.2006.887903

J. Bibliography-coron, B. B. D-'andréa-novel, and G. Bastin, Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems, SIAM Journal on Control and Optimization, vol.47, issue.3, pp.1460-1498, 2008.
DOI : 10.1137/070706847

R. F. Curtain, Linear-quadratic control problem with fixed endpoints in infinite dimensions, Journal of Optimization Theory and Applications, vol.16, issue.1, pp.55-74, 1984.
DOI : 10.1007/BF00934894

R. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, 1995.
DOI : 10.1007/978-1-4612-4224-6

M. Dick, M. Gugat, and G. Leugering, Classical solutions and feedback stabilization for the gas flow in a sequence of pipes, Networks and Heterogeneous Media, pp.691-709, 2010.

S. Dubljevic, N. H. El-farra, P. Mhaskar, and P. D. Christofides, Predictive control of parabolic PDEs with state and control constraints, International Journal of Robust and Nonlinear Control, vol.50, issue.16, pp.749-772, 2006.
DOI : 10.1002/rnc.1097

S. Dubljevic, P. Mhaskar, N. H. El-farra, and P. D. Christofides, Predictive control of transport-reaction processes, Computers & Chemical Engineering, vol.29, issue.11-12, pp.2335-2345, 2005.
DOI : 10.1016/j.compchemeng.2005.05.008

S. Dubljevic, P. Mhaskar, N. H. El-farra, and P. D. Christofides, Predictive control of transport-reaction processes, Computers & Chemical Engineering, vol.29, issue.11-12, pp.2335-2345, 2005.
DOI : 10.1016/j.compchemeng.2005.05.008

S. Dubljevic, N. H. El-farra, P. M. Christofides, and P. D. , Predictive control of parabolic PDEs with state and control constraints, International Journal of Robust and Nonlinear Control, vol.50, issue.16, pp.749-772, 2006.
DOI : 10.1002/rnc.1097

J. Dulhoste, D. Georges, and G. Besançon, Nonlinear Control of Open-Channel Water Flow Based on Collocation Control Model, Journal of Hydraulic Engineering, vol.130, issue.3, pp.254-266, 2004.
DOI : 10.1061/(ASCE)0733-9429(2004)130:3(254)

H. O. Fattorini, Infinite dimensional optimization and control theory, 1999.
DOI : 10.1017/CBO9780511574795

R. Findeisen and F. Allgöwer, An introduction to nonlinear model predictive control, Proceedings of 21st Benelux Meeting on Systems and Control', 2002.

R. Findeisen, L. Imsland, F. Allgöwer, and B. A. Foss, Output feedback stabilization of constrained systems with nonlinear predictive control, International Journal of Robust and Nonlinear Control, vol.4, issue.12, pp.211-227, 2003.
DOI : 10.1002/rnc.814

R. Bibliography-findeisen, L. Imsland, F. Allgöwer, and B. A. Foss, State and output feedback nonlinear model predictive control: An overview, European Journal of Control, vol.9, issue.3, pp.179-195, 2003.

C. E. García, D. M. Prett, and M. Morari, Model predictive control: Theory and practice???A survey, Automatica, vol.25, issue.3, pp.335-348, 1989.
DOI : 10.1016/0005-1098(89)90002-2

D. Georges, Infinite-dimensional nonlinear predictive control design for openchannel hydraulic systems, Networks and Heterogeneous Media, pp.1-18, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00384966

W. H. Graf and M. Altinakar, Hydraulique fluviale -Écoulement et phénomènes de transport dans les canaux à géométrie simple, 2000.

J. Greenberg and T. Li, The effect of boundary damping for the quasi-linear wave equation, Journal of differential equation, vol.22, pp.66-75, 1984.

L. Grüne, J. Pannek, M. Seehafer, and K. Worthmann, Analysis and Design of Unconstrained Nonlinear MPC Schemes for Finite and Infinite Dimensional Systems, SIAM Journal on Control and Optimization, vol.48, issue.2, pp.1206-1228, 2009.
DOI : 10.1137/070707853

J. D. Halleux, C. Prieur, J. Coron, B. B. D-'andréa-novel, and G. Bastin, Boundary feedback control in networks of open channels, Automatica, vol.39, issue.8, pp.1365-1376, 2003.
DOI : 10.1016/S0005-1098(03)00109-2

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, 1995.
DOI : 10.1137/1037043

K. Ito and K. Kunisch, Receding horizon optimal control for infinite dimensional systems', ESAIM: Control, Optimisation and Calculus of Variations 8, pp.741-760, 2002.

D. Jacquet, Modélisation macroscopique du traffic et contrôle des lois de conservation non linéaires associées, 2006.

M. Junk and M. Rheinlainder, Regular and multiscale expansions of a lattice Boltzmann method, Progress in Computational Fluid Dynamics, 2008.
DOI : 10.1504/PCFD.2008.018076

D. E. Kirk, Optimal control theory -An introduction, 1998.

M. Krstic and A. Smyshlyaev, Backstepping boundary control for first order hyperbolic PDEs and application to systems with actuator and sensor delays, 2007 46th IEEE Conference on Decision and Control, pp.750-758, 2008.
DOI : 10.1109/CDC.2007.4434474

I. Lasiecka and R. Triggiani, Control Theory for Partial Diffrential Equations: Continuous and Approximation Theories Volume II Abstract Hyperbolic-like Systems over a Finite Time Horizon, 2000.

T. Li and B. Rao, Exact Boundary Controllability of Unsteady Flows in a Tree-like Network of Open Canals, Methods and Applications of Analysis, vol.11, issue.3, pp.353-366, 2004.
DOI : 10.4310/MAA.2004.v11.n3.a7

T. T. Li, B. Rao, and Y. Lin, Semi-global C1 solution and exact boundary controllability for reducible quasilinear hyperbolic systems', Modélisation mathématique et analyse numérique, pp.399-408, 2000.

M. J. Lighthill and G. B. Whitham, On Kinematic Waves. II. A Theory of Traffic Flow on Long Crowded Roads, Proceedings of the Royal Society of, 1955.
DOI : 10.1098/rspa.1955.0089

X. Litrico and V. Fromion, Boundary control of linearized saint-venant equations oscillating modes, Proceeding of the 43rd IEEE Conference on Decision and Control, 2004.

X. Litrico and V. Fromion, Boundary control of hyperbolic conservation laws using a frequency domain approach, Automatica, vol.45, issue.3, pp.647-656, 2009.
DOI : 10.1016/j.automatica.2008.09.022

X. Litrico and V. Fromion, Modeling and Control of Hydrosystems -A Frequency Domain Approach, 2009.

J. Liu, D. M. Na, P. D. Christofides, and J. F. Davis, Lyapunov-based model predictive control of nonlinear systems subject to time-varying measurement delays, International Journal of Adaptive Control and Signal Processing, vol.39, issue.9, pp.788-807, 2009.
DOI : 10.1002/acs.1085

D. Q. Mayne and H. Michalska, Receding horizon control of nonlinear systems, IEEE Transactions on Automatic Control, vol.35, issue.7, pp.814-824, 1990.
DOI : 10.1109/9.57020

D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. Scokaert, Constrained model predictive control: Stability and optimality, pp.789-814, 2000.
DOI : 10.1016/s0005-1098(99)00214-9

P. Mhaskar, N. H. El-farra, and P. D. Christofides, Predictive control of switched nonlinear systems with scheduled mode transitions, IEEE Transactions on Automatic Control, vol.50, issue.11, pp.1670-1680, 2005.
DOI : 10.1109/TAC.2005.858692

P. Mhaskar, N. H. El-farra, and P. D. Christofides, Stabilization of nonlinear systems with state and control constraints using lyapunov-based predictive control', Systems and Control Letters 55, pp.650-659, 2006.

H. Michalska and D. Q. Mayne, Moving horizon observers and observer-based control, IEEE Transactions on Automatic Control, vol.40, issue.6, pp.995-1006, 1995.
DOI : 10.1109/9.388677

L. Mohammadi, S. Dubljevic, and J. F. Forbes, Robust characteristic-based MPC of a fixed-bed reactor, Proceedings of the 2010 American Control Conference, 2010.
DOI : 10.1109/ACC.2010.5531050

A. Pazy, Semigroups of linear operators and Application to Partial Differential Equations, of Applied Mathematical Sciences, 1983.
DOI : 10.1007/978-1-4612-5561-1

V. Pham, B. Chopard, L. Lefèvre, D. A. Ondo, and E. Mendes, Study of the 1d lattice boltzmann shallow water equation and its coupling to build a canal network, Journal of Computational Physics, vol.229, pp.7373-7400, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00580905

V. Pham, D. Georges, and G. Besançon, Infinite-dimensional Receding Horizon Optimal Control for an Open-channel System, Proceedings of 8th IFAC Symposium on Nonlinear Control Systems, 2010.
DOI : 10.3182/20100901-3-IT-2016.00216

URL : https://hal.archives-ouvertes.fr/hal-00551277

V. Pham, D. Georges, and G. Besançon, On the Use of a Global Control Lyapunov Functional in Infinite-dimensional Predictive Control, Proceedings of 4th IFAC Symposium on System, Structure and Control', 2010.
DOI : 10.3182/20100915-3-IT-2017.00055

URL : https://hal.archives-ouvertes.fr/hal-00551288

V. Pham, D. Georges, and G. Besançon, Predictive Control with guaranteed stability for hyperbolic systems of conservation laws, 49th IEEE Conference on Decision and Control (CDC), 2010.
DOI : 10.1109/CDC.2010.5718009

URL : https://hal.archives-ouvertes.fr/hal-00551283

V. Pham, D. Georges, and G. Besançon, Receding Optimal Boundary Control of Non-linear Hyperbolic Systems of Conservation Laws, Proceedings of 18th World Congress of the International Federation of Automatic Control, 2011.
DOI : 10.3182/20110828-6-IT-1002.01027

URL : https://hal.archives-ouvertes.fr/hal-00620464

V. Pham, D. Georges, and G. Besançon, Analyse de stabilité de la commande prédictive d'une classe de lois de conservation, Proceedings of Septième Conférence Internationale Francophone d'Automatique, 2012.

V. Pham, D. Georges, and G. Besançon, Predictive control with guaranteed stability for water hammer equations, IEEE transactions on automatic control, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00937483

V. Pham, D. Georges, and G. Besançon, Predictive Control with terminal constraint for 2×2 hyperbolic systems of conservation laws, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012.
DOI : 10.1109/CDC.2012.6426538

V. Pham, D. Georges, and G. Besançon, Receding horizon boundary control of nonlinear conservation laws with shockavoidance, Automatica, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00692041

V. T. Pham, D. Georges, and G. Besançon, Commande prédictive avec stabilité pour une classe de systèmes de lois de conservation', JESA -Numéro spécial sur la commande prédictive, 2012.

V. T. Pham, D. Georges, and G. Besançon, Infinite-dimensional predictive control for hyperbolic systems', revised version, 2012.

C. Prieur, Control of systems of conservation laws with boundary errors, Networks and Heterogeneous Media, pp.393-407, 2009.
DOI : 10.3934/nhm.2009.4.393

URL : https://hal.archives-ouvertes.fr/hal-00392197

C. Prieur, J. Winkin, and G. Bastin, Robust boundary control of systems of conservation laws, Mathematics of Control, Signals, and Systems, vol.124, issue.1, pp.173-197, 2008.
DOI : 10.1007/s00498-008-0028-x

J. A. Primbs, Nonlinear optimal control: A receding horizon approach, 1999.

J. Rauch, L2 is a continuable initial condition for kreiss' mixed problems, Communications on Pure and Applied Mathematics pp, pp.265-285, 1972.
DOI : 10.1002/cpa.3160250305

J. B. Rauch and F. J. Massey, Differentiability of solution to hyperbolic initial boundary value problems', Transactions of the, pp.303-318, 1974.

J. Rauch and M. Taylor, Exponential Decay of Solutions to Hyperbolic Equations in Bounded Domains, Indiana University Mathematics Journal, vol.24, issue.1, pp.79-86, 1974.
DOI : 10.1512/iumj.1975.24.24004

D. Russell, Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions, SIAM Review, vol.20, issue.4, pp.639-739, 1978.
DOI : 10.1137/1020095

D. L. Russell, Quadratic Performance Criteria in Boundary Control of Linear Symmetric Hyperbolic Systems, SIAM Journal on Control, vol.11, issue.3, pp.475-509, 1973.
DOI : 10.1137/0311039

B. Saint-venant, Théorie du mouvement non permanent des eaux avec application aux crues des rivières et à l'introduction des marées dans leur lit, 1871.

V. D. Santos, B. Maschke, and Y. L. Gorec, A Hamintonian perspective to the stabilization of systems of two conservation laws, pp.249-266, 2009.

V. D. Santos and C. Prieur, Boundary Control of Open Channels With Numerical and Experimental Validations, IEEE Transactions on Control Systems Technology, vol.16, issue.6, pp.1252-1264, 2008.
DOI : 10.1109/TCST.2008.919418

R. Sargent, Optimal control, Journal of Computational and Applied Mathematics, vol.124, issue.1-2, pp.361-371, 2000.
DOI : 10.1016/S0377-0427(00)00418-0

E. Schechter, Evolution generated by semilinear dissipative plus compact operators' , Transactions of the, pp.297-308, 1983.

D. Serre, Systèmes de lois de conservation I, Diderot Editeur, Arts et Sciences, 1996.

D. Serre, Systems of Conservation law 1: Hyperbolicity, entropies, shock waves, 1999.
DOI : 10.1017/CBO9780511612374

H. Shang, J. F. Forbes, and M. Guay, Feedback control of hyperbolic distributed parameter systems, Chemical Engineering Science, vol.60, issue.4, pp.969-980, 2005.
DOI : 10.1016/j.ces.2004.09.067

H. Shang, J. F. Forbes, and M. Guay, Computationally efficient model predictive control for convection dominated parabolic systems, Journal of Process Control, vol.17, issue.4, pp.379-386, 2007.
DOI : 10.1016/j.jprocont.2006.09.009

R. Szymkiewicz, Numerical modeling in Open Channel Hydraulics, of Water Science and Technology Library, 2010.
DOI : 10.1007/978-90-481-3674-2

R. Vazquez, M. Krstic, and J. Coron, Backstepping boundary stabilization and state estimation of a 2x2 linear hyperbolic system, Proceedings of 50th IEEE Conference on Decicion and Control and European Control Conference, 2011.

Z. Wang, Global exact controllability for quasilinear hyperbolic systems of diagonal form with linearly degenerate characteristics', Nonlinear Analysis 69, pp.510-522, 2008.

C. Xu and G. Sallet, Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems', ESAIM: Control, Optimization and Calculus of Variations 7, pp.421-442, 2002.

J. Yong, Existence theory of optimal controls for distributed parameter systems, Kodai Mathematical Journal, vol.15, issue.2, pp.193-220, 1992.
DOI : 10.2996/kmj/1138039597

E. Zuazua, Controllability of partial differential equations and its semi-discrete approximations', Discrete and continuous dynamical systems, pp.469-513, 2002.

E. Zuazua, Optimal and approximate control of finite-difference approximation schemes for the 1-d wave equation, Rendiconti di Matematica, vol.24, issue.2, pp.201-237, 2004.

H. Zwart, Y. L. Gorrec, B. Maschke, and J. Villegas, Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain, ESAIM: Control, Optimisation and Calculus of Variations, pp.1077-1093, 2009.
DOI : 10.1051/cocv/2009036