H. Banks and K. Ito, A Numerical Algorithm for Optimal Feedback Gains in High Dimensional Linear Quadratic Regulator Problems, SIAM Journal on Control and Optimization, vol.29, issue.3, pp.499-515, 1991.
DOI : 10.1137/0329029

H. Banks and K. Kunisch, The Linear Regulator Problem for Parabolic Systems, SIAM Journal on Control and Optimization, vol.22, issue.5, pp.684-698, 1984.
DOI : 10.1137/0322043

P. Benner, Solving large-scale control problems, IEEE Control Systems Magazine, vol.24, issue.1, pp.44-59, 2004.
DOI : 10.1109/MCS.2004.1272745

P. Benner and S. Görner, MPC for the Burgers equation based on an LGQ design, Proc. Appl. Math. Mech, vol.6, issue.1, pp.781-782, 2006.

P. Benner and S. Hein, Model predictive control based on an LQG design for time-varying linearizations, pp.1-201000221, 2009.

P. Benner and S. Hein, Model Predictive Control for Nonlinear Parabolic Differential Equations Based on a Linear Quadratic Gaussian Design, PAMM, vol.9, issue.1, pp.613-614, 2009.
DOI : 10.1002/pamm.200910278

P. Benner, J. R. Li, and T. Penzl, Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems, Numerical Linear Algebra with Applications, vol.81, issue.1, pp.755-777, 2008.
DOI : 10.1002/nla.622

URL : https://hal.archives-ouvertes.fr/hal-00781119

P. Benner and J. Saak, Linear-quadratic regulator design for optimal cooling of steel profiles, Sonderforschungsbereich 393 Parallele Numerische Simulation für Physik und Kontinuumsmechanik, p.9107

P. Benner and J. Saak, A Galerkin-Newton-ADI Method for Solving Large-Scale Algebraic Riccati Equations. Preprint SPP1253-090, DFG Priority Program " Optimization with Partial Differential Equations, 2010.

E. Camacho and C. Bordons, Model Predictive Control Advanced Textbooks in Control and Signal Processing, 2004.

R. Curtain and T. Pritchard, Infinite Dimensional Linear System Theory, Lecture Notes in Control and Information Sciences, vol.8, 1978.
DOI : 10.1007/BFb0006761

B. Datta, Numerical Methods for Linear Control Systems, 2004.

K. L. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, Semigroup Forum, vol.63, issue.2, 2000.
DOI : 10.1007/s002330010042

L. Grüne and J. Pannek, Nonlinear Model Predictive Control: Theory and Algorithms, 2011.

S. Hein and . Tu-chemnitz, MPC/LQG-Based Optimal Control of Nonlinear Parabolic PDEs, Department of Mathematics, pp.1-201000134, 2010.

K. Ito and K. Kunisch, Asymptotic Properties of Receding Horizon Optimal Control Problems, SIAM Journal on Control and Optimization, vol.40, issue.5, pp.1455-1472, 2001.
DOI : 10.1137/S0363012900369423

K. Ito and K. Kunisch, Receding horizon optimal control for infinite dimensional systems, ESAIM: Control, Optimisation and Calculus of Variations, vol.8, pp.741-760, 2002.
DOI : 10.1051/cocv:2002032

K. Ito and K. Kunisch, Receding Horizon Control with Incomplete Observations, SIAM Journal on Control and Optimization, vol.45, issue.1, pp.207-225, 2006.
DOI : 10.1137/S0363012903437988

R. Kalman and R. Bucy, New Results in Linear Filtering and Prediction Theory, Journal of Basic Engineering, vol.83, issue.1, pp.95-108, 1961.
DOI : 10.1115/1.3658902

K. Morris and C. Navasca, Solution of algebraic Riccati equations arising in control of partial differential equations. In: Control and boundary analysis, Lect. Notes Pure Appl. Math, vol.240, pp.257-280, 2005.