L. Commande and .. Des-mdàmd-`-mdà-réponse-non-instantanée, 171 6.2.1 Développement du critère d'optimisation, p.184

L. Correia, Unétatà 10 composantes est obtenu, alors que´ etatàetat`etatà 8 composantes. C'est d'ailleurs cettedernì ere version qui est présentée dans ce mémoire Une dynamique du premier ordre pour la perturbation et la dynamique des MD est analysée. Des courbes de performance enénergieen´enénergie cohérente en fonction de la constante de temps du MD y sont présentées afin de montrer l'apport de la commande optimale 2010] généralisent ensuite le formalisme aux modèles d'ordre deux et l'utilisent dans le cadre de l'application au ELT Européen o` u les perturbation sont celles dû au vent, donc de variance bien plusélevéeplus´plusélevée que les perturbation de phase d'origine purement atmosphérique. Ce cas particulier est traité dans la section suivante. L'article soumis [Correia et al., 2009c] reprend la formulation de l'article précédent en rajoutant uné etude de robustesse et des explications supplémentaires sur la commande modale des MD avec dynamique non négligeable. L'innovation par rapport aux cas considérés précédemment est l'inclusion des perturbations dues au vent, déjà discutéesdiscutées`discutéesà la section 6, 2008.

E. Le and . Européen, dynamiques du second ordre L'ELT Européen est un télescope adaptatif : sa conception optique inclut en effet plusieurs miroirs pré-focaux [Gilmozzi et Spyromilio Plus précisément le couple M4/M5 est composé d'un miroir avec 5000-7000 actionneurs et d'un miroir, en l'occurrence M5, 2008.

. Gasmi, Les modèlesmodèles`modèlesàmodèlesà´modèlesàéléments finis actuels ne considèrent pas les supports des miroirs ni l'ensemble de la structure mécanique Une discussion plusélargieplus´plusélargie sur la modélisation des composant adaptatifs se trouve dans L'ensemble des résultats dans cette section ont fait objet de l'article [Correia et al., 2010]. Les résultats principaux présentés dans le cadre de cet article sont rappelés dans les deux sous-sections suivantes, 2008.

. Le-régulateurrégulateur´régulateurétant-synthétisésynthétisé, synthétiséà partir de ces paramètres identifiés, il s'agit donc d'un cas de cohérence perturbation/modèle pour la commande

C. Revuesàrevues-`-revuesà-comité-de-lecture, H. Correia, C. Raynaud, J. Kulcsár, and . Conan, On the optimal wave-front reconstruction and control in Adaptive Optics with mirror dynamics, Journal of the Optical Society of America A (JOSA A), vol.26, issue.2, pp.333-349, 2010.

H. Raynaud, C. Correia, C. Kulcsár, and J. Conan, Minimum variance control of astronomical adaptive optics systems with actuator dynamics under synchronous and asynchonous sampling, International Journal of Robust and Nonlinear Control

C. Correia, H. Raynaud, C. Kulcsár, and J. Conan, Minimum-variance control for the woofertweeter concept, Journal of the Optical Society

C. Correia, Minimum-variance wave-front control with resonant deformable mirrors, soumis au numéro spécial du European Journal of Control, 2010.
DOI : 10.3166/ejc.17.222-236

C. Comptes-rendus-de-conférences-internationales, H. Correia, C. Raynaud, J. Kulcsár, and . Conan, Accounting for mirror dynamics in optimal adaptive optics control, Proceedings of the European Control Conference, 2009.

C. Correia, H. Raynaud, C. Kulcsár, and J. Conan, Minimum-variance control for the woofertweeter concept, 2009.

C. Kulcsár, H. Raynaud, J. Conan, C. Correia, and C. Petit, Control Design and Turbulent Phase Models in Adaptive Optics: A State-Space Interpretation, Frontiers in Optics 2009/Laser Science XXV/Fall 2009 OSA Optics & Photonics Technical Digest, 2009.
DOI : 10.1364/AOPT.2009.AOWB1

C. Correia, J. Conan, C. Kulcsár, H. Raynaud, and C. Petit, Adapting optimal LQG methods to ELT-sized AO systems, 1st AO4ELT conference, Adaptive Optics for Extremely Large Telescopes, 2009.
DOI : 10.1051/ao4elt/201007003

F. Quirós-pacheco, C. Correia, and S. Esposito, Fourier transform-wavefront reconstruction for the pyramid wavefront sensor, 1st AO4ELT conference, Adaptive Optics for Extremely Large Telescopes, 2009.
DOI : 10.1051/ao4elt/201007005

I. Montilla, C. Béchet, M. Lelouarn, C. Correia, M. Tallon et al., Comparison of Reconstruction and Control algorithms on the ESO end-to-end simulator OCTOPUS, 1st AO4ELT conference, Adaptive Optics for Extremely Large Telescopes, 2009.
DOI : 10.1051/ao4elt/201003002

C. Correia, H. Raynaud, C. Kulcsár, and J. Conan, Globally optimal minimum-variance Annexes control in adaptive optics systems with mirror dynamics, Proceedings of the SPIE -Ground-based Astronomical Instrumentation, 2008.

C. Correia, C. Kulcsár, J. Conan, and H. Raynaud, Analytical Hartmann-Shack modelling in the Fourier domain ; Application to real-time reconstruction in Adaptive Optics, Proceedings of the SPIE -Ground-based Astronomical Instrumentation, 2008.

H. Raynaud, C. Kulcsár, C. Correia, and J. Conan, Multi-rate LQG AO control, Proceedings of the SPIE -Ground-based Astronomical Instrumentation, 2008.
DOI : 10.1117/12.789231

C. Correia, J. Conan, C. Kulcsár, H. Raynaud, C. Petit et al., Fourier-domain wavefront reconstruction for large adaptive optical systems, 2007.

. Bibliographie-[-aller-carpentier, High order test bench for extreme adaptive optics system optimization, Proc. of the SPIE, pp.70153-79, 2008.

A. , M. Anderson, B. D. Et-moore, and J. B. , Optimal Control, Linear Quadratic Methods, p.179, 1995.

A. , M. Anderson, B. D. Et-moore, and J. B. , Optimal Filtering, p.134, 1995.

. Ardeberg, A European ELT design study The Scientific Requirements for Extremely Large Telescopes, IAU Symposium, vol.232, pp.432-442, 2006.

. Arsenault, A deformable secondary mirror for the VLT, Advances in Adaptive Optics II, pp.62720-169, 2006.
DOI : 10.1117/12.672879

E. Arthur-gelb-arthur-gelb, Applied Optimal Estimation. The M.I.T press, p.57, 1974.

. Assémat, Method for simulating infinitely long and non stationary phase screens with optimized memory storage, Optics Express, vol.14, issue.3, pp.988-999, 2006.
DOI : 10.1364/OE.14.000988

H. W. Babcock, The Possibility of Compensating Astronomical Seeing, Publications of the Astronomical Society of the Pacific, vol.65, pp.229-263, 1953.
DOI : 10.1086/126606

. Bar-shalom, . Tse, Y. Bar-shalom, and E. Et-tse, Dual effect, certainty equivalence, and separation in stochastic control, IEEE Transactions on Automatic Control, vol.19, issue.5, pp.494-500, 1974.
DOI : 10.1109/TAC.1974.1100635

J. D. Barchers, Multigrid Approach to Predictive Wave-Front Reconstruction in Adaptive Optical Systems, Applied Optics, vol.43, issue.18, pp.3708-3716, 2004.
DOI : 10.1364/AO.43.003708

C. Béchet, Commande optimale rapide pour l'optique adaptative des futurs télescopes hectométriques, p.126, 2008.

. Béchet, Comparison of minimum-norm maximum likelihood and maximum a posteriori wavefront reconstructions for large adaptive optics systems, Journal of the Optical Society of America A, vol.26, issue.3, pp.26497-508, 2009.
DOI : 10.1364/JOSAA.26.000497

. Béchet, FRIM: minimum-variance reconstructor with a fractal iterative method, Advances in Adaptive Optics II, pp.62722-62739, 2006.
DOI : 10.1117/12.672197

B. Béchet, Closed-Loop AO Performance with FrIM, Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, pp.93-131, 2007.
DOI : 10.1364/AOPT.2007.JTuA4

J. M. Beckers, Increasing the size of the isoplanatic patch with multiconjugate adaptive optics, ESO Conference on Very Large Telescopes and their Instrumentation, pp.693-703, 1988.

. Beghi, A comparison of Kalman filter based algorithms for turbulent phase control in an adaptive optics system, 2008 47th IEEE Conference on Decision and Control, pp.1839-1844, 2008.
DOI : 10.1109/CDC.2008.4738739

. Beghi, A Markov-Random-Fieldbased approach to modeling and prediction of atmospheric turbulence, Proc. of the 16th Mediterranean Conference on Control and Automation, pp.1735-1740, 2008.

. Beghi, On the estimation of atmospheric turbulence layers, Proc. of the 17th IFAC World Congress, pp.8984-8989, 2008.
DOI : 10.3182/20080706-5-KR-1001.01517

. Beghi, Stochastic realization approach to the efficient simulation of phase screens, Journal of the Optical Society of America A, vol.25, issue.2, pp.515-525, 2008.
DOI : 10.1364/JOSAA.25.000515

. Beuzit, SPHERE: a 'Planet Finder' instrument for the VLT, Ground-based and Airborne Instrumentation for Astronomy II, pp.29-53, 2006.
DOI : 10.1117/12.790120
URL : https://hal.archives-ouvertes.fr/hal-00416982

J. L. Beuzit-et-hubin-]-beuzit and N. Et-hubin, ADONIS -a user friendly adaptive optics system for the 3.6-m telescope. The Messenger, pp.52-53, 1993.

R. Bowman, K. W. Bowman, and W. T. Et-rhodes, Application of wavelets to wavefront reconstruction in adaptive optical systems, Proc. of the SPIE, pp.288-299, 1997.

T. J. Brennan-et-rhoadarmer-]-brennan and T. A. Et-rhoadarmer, Performance of a woofertweeter deformable mirror control architecture for high-bandwidth high-spatial resolution adaptive optics, Proc. of the SPIE, pp.63060-186, 2006.

T. A. Brummelaar, The contribution of high order Zernike modes to wavefront tilt, Optics Communications, vol.115, issue.5-6, pp.417-424, 1995.
DOI : 10.1016/0030-4018(95)00053-B

. Burrus, Introduction to Wavelets and Wavelet Transforms : a primer, p.61, 1998.

. Charton, System level simulation of micro-mirrors for adaptive optics, Specialized Optical Developments in Astronomy, pp.207-218, 2003.
DOI : 10.1117/12.458104

. Chauvin, A giant planet candidate near a young brown dwarf, Direct VLT/NACO observations using IR wavefront sensing, pp.29-32, 2004.
DOI : 10.1051/0004-6361:200400056

R. Conan, Modélisation des effets de l'´ echelle externe de cohérence spatiale du front d'onde pour l'observation en Haute Résolution Angulaire en Astronomie, p.30, 2000.

C. Correia, Multi-stage reconstructor, p.61, 2006.

. Correia, Fourier-domain wave-front reconstruction for large adaptive optical systems, pp.73-78, 2007.

. Correia, Hartmann modelling in the discrete spatial-frequency domain: application to real-time reconstruction in adaptive optics, Adaptive Optics Systems, pp.701551-71, 2008.
DOI : 10.1117/12.788455

. Correia, On the optimal reconstruction and control of adaptive optical systems with mirroir dynamics, J. Opt. Soc. Am. A, vol.204, issue.2, pp.27333-349, 2010.

. Correia, Globally optimal minimum mean-square error control in adaptive optical systems with mirror dynamics, Adaptive Optics Systems, pp.70151-204, 0199.
DOI : 10.1117/12.788459

. Correia, Accounting for mirror dynamics in optimal adaptive optics control, Proc. of the European Control Conference, p.213, 0199.

. Correia, Minimumvariance control for astronomical adaptive optics with resonant deformable mirrors, In European Journal of Control, p.204, 2009.

. Correia, Minimum Variance Control for the Woofer-Tweeter Concept, Frontiers in Optics 2009/Laser Science XXV/Fall 2009 OSA Optics & Photonics Technical Digest, pp.4-204, 2009.
DOI : 10.1364/AOPT.2009.AOWB4

A. Costille, Les optiques adaptatives grand champ : Stratégie de correction et validations expérimentales, p.162, 2009.

. Costille, Wide field adaptative optics laboratory demonstration with closed loop tomographic control, J. Opt. Soc. Am. A, vol.107, 2009.

G. Dai, Modal compensation of atmospheric turbulence with the use of Zernike polynomials and Karhunen???Lo??ve functions, Journal of the Optical Society of America A, vol.12, issue.10, pp.2182-2193, 1995.
DOI : 10.1364/JOSAA.12.002182

G. Dai, Wavefront expansion basis functions and their relationships, Journal of the Optical Society of America A, vol.23, issue.7, pp.1657-1668, 2006.
DOI : 10.1364/JOSAA.23.001657

. Dessenne, Modal prediction for closed-loop adaptive optics, Optics Letters, vol.22, issue.20, pp.1535-1537, 1997.
DOI : 10.1364/OL.22.001535

. Dessenne, Optimization of a predictive controller for closed-loop adaptive optics, Applied Optics, vol.37, issue.21, pp.4623-4633, 1998.
DOI : 10.1364/AO.37.004623

. Dessenne, Optimization of a predictive controller for closed-loop adaptive optics, Applied Optics, vol.37, issue.21, pp.4623-4633, 1998.
DOI : 10.1364/AO.37.004623

. Dessenne, Sky implementation of modal predictive control in adaptive optics, Optics Letters, vol.24, issue.5, pp.339-341, 1999.
DOI : 10.1364/OL.24.000339

R. H. Dicke, Phase-contrast detection of telescope seeing errors and their correction, The Astrophysical Journal, vol.198, issue.16, pp.605-615, 1975.
DOI : 10.1086/153639

. Diolaiti, Identification and rejection of waffle modes in layer-oriented adaptive optics, Adaptive Optical System Technologies II, pp.1001-1010, 2003.
DOI : 10.1117/12.458960

. Dowla, <title>Fast Fourier and wavelet transforms for wavefront reconstruction in adaptive optics</title>, High-Resolution Wavefront Control: Methods, Devices, and Applications II, pp.118-127, 2000.
DOI : 10.1117/12.407495

B. L. Ellerbroek, First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes, Journal of the Optical Society of America A, vol.11, issue.2, pp.783-805, 1994.
DOI : 10.1364/JOSAA.11.000783

B. L. Ellerbroek, Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques, Journal of the Optical Society of America A, vol.19, issue.9, pp.1803-1816, 2002.
DOI : 10.1364/JOSAA.19.001803

. Ellerbroek, A computationally efficient wavefront reconstructor for simulation of multi-conjugate adaptive optics on giant telescopes, Adaptive Optical System Technologies II Proc. of the SPIE, pp.989-1000, 2003.

. Ellerbroek, Optimizing closed-loop adaptive-optics performance with use of multiple control bandwidths, Journal of the Optical Society of America A, vol.11, issue.11, pp.2871-2886, 1994.
DOI : 10.1364/JOSAA.11.002871

. Ellerbroek, . Vogel, B. L. Ellerbroek, and C. R. Vogel, Inverse problems in astronomical adaptive optics, Inverse Problems, vol.25, issue.6, pp.25-68, 2009.
DOI : 10.1088/0266-5611/25/6/063001

E. M. Ellis, Low-cost Bimorph Mirrors in Adaptive Optics, p.193, 1999.

F. Et-koliopoulos-]-freischlad, K. R. Et-koliopoulos, and C. L. , Modal estimation of a wave front from difference measurements using the discrete Fourier transform, J. Opt. Soc, 1986.

D. Fried, D. L. Fried, T. Fusco, and . Fusco, Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements ´ Etude de la correction partielle en optique adaptative Efficient phase estimation for large-field-of-view adaptive optics Optimal wave-front reconstruction strategies for multiconjugate adaptive optics Modeling of a large deformable mirror for future E-ELT Suppressing anomalous localized waffle behavior in least-squares wavefront reconstructors Tomography for multiconjugate adaptive optics systems using laser guide stars Astronomical adaptive optics I : Modal control optimization, Proc. of the SPIE Proc. of the SPIE - Adaptive Optical System Technologies II Proc. of the SPIE, pp.551427-1435370, 1965.

I. Astronomical-adaptive-optics, R. Gerchberg, I. I. Gikhman, A. V. Et-skorokhod, L. Gilles et al., Super-resolution through error energy reduction Introduction to the Theory of Random Processes Order-n sparse minimum-variance open-loop reconstructor for extreme adaptive optics Sparse minimum-variance open-loop reconstructors for extreme adaptive optics : order n multigrid versus preordered cholesky factorization Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multiconjugate adaptive optics Shack-hartmann wavefront sensing with elongated sodium laser beacons : centroiding versus matched filtering Layer-oriented multigrid wavefront reconstruction algorithms for multi-conjugate adaptive optics, Astronomy and Astrophysics Supplement Series Proc. of the SPIE Proc. of the SPIE, pp.153-49709, 1974.

. Gilles, Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics, Applied Optics, vol.42, issue.26, pp.5233-5250, 2003.
DOI : 10.1364/AO.42.005233

. Gilles, Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction, Journal of the Optical Society of America A, vol.19, issue.9, pp.1817-1822, 2002.
DOI : 10.1364/JOSAA.19.001817

. Gilmozzi, . Spyromilio, R. Gilmozzi, and J. Et-spyromilio, The 42m European ELT: status, Ground-based and Airborne Telescopes II, pp.701219-204, 2008.
DOI : 10.1117/12.790801

G. Et-ryshik-]-gradstein, I. S. Et-ryshik, and I. H. , Tables of Series, Products and Integrals, p.27, 1981.

W. Hackbusch, Multi-grid Methods with Applications, p.150, 1985.
DOI : 10.1007/978-3-662-02427-0

. Hallibert, Optical design for the adaptive secondary setup and instrument stimulator (ASSIST), Current Developments in Lens Design and Optical Engineering VII, pp.62880-169, 2006.
DOI : 10.1117/12.680560

. Hampton, Wavefront reconstruction over a circular aperture using gradient data extrapolated via the mirror equations, Applied Optics, vol.48, issue.20, 2009.
DOI : 10.1364/AO.48.004018

. Hampton, Control of a woofer tweeter system of deformable mirrors, Advanced Software and Control for Astronomy, pp.62741-187, 2006.
DOI : 10.1117/12.672451

. Harding, Fast simulation of a kolmogorov phase screen, Applied Optics, vol.38, issue.11, pp.2161-2170, 1999.
DOI : 10.1364/AO.38.002161

. Herriot, NFIRAOS: TMT narrow field near-infrared facility adaptive optics, Advances in Adaptive Optics II, pp.62720-207, 2006.
DOI : 10.1117/12.672337

J. Herrmann, Least-squares wave front errors of minimum norm, Journal of the Optical Society of America, vol.70, issue.1, pp.28-35, 1980.
DOI : 10.1364/JOSA.70.000028

J. Herrmann, Phase variance and Strehl ratio in adaptive optics, Journal of the Optical Society of America A, vol.9, issue.12, pp.2257-2258, 1992.
DOI : 10.1364/JOSAA.9.002257

. Horsleya, Characterization of a bimorph deformable mirror using stroboscopic phase-shifting interferometry, Sensors and Actuators A : Physical, pp.28-193, 2007.
DOI : 10.1016/j.sna.2006.04.052

. Hubin, Technical specifications for the M4 adaptive unit of the E-ELT : conceptual design, prototyping and preliminary design study, p.210, 2007.

R. H. Hudgin, R. H. Hudgin, R. H. Hudgin, K. J. Jones, K. J. Jones et al., Optimal wave-front estimation Wave-front compensation error due to finite corrector-element size Wave-front reconstruction for compensated imaging Wavelet-based adaptive optics Wavelet-based wavefront control Wavelet-based phase determination in optical turbulence On linear control theory, Proc. of the SPIE Proc. of the SPIE Proc. of the SPIE, pp.378-382, 1961.

W. Hardy, ]. W. Hardy, R. E. Kalman, T. V. Kármán, and . Kasper, Adaptive Optics for Astronomical Telescopes A new approach to linear filtering and prediction problems Transcribed into electronic form by John Lukesh Progress in the statistical theory of turbulence Fast calibration of high-order adaptive optics systems Mid-infrared instrumentation for the european extremely large telescope, Proc. Nat. Acad. Sci. Proc. of the SPIE Dissipation of energy in the locally isotropic turbulence. Comptes rendus (Doklady) de l'Académie des Sciences de l'U.R.S.S, pp.6835-6880, 1941.

. Kulcsár, Control design and turbulent phase models in adaptive optics : A state-space interpretation In Adaptive Optics : Methods, Analysis and Applications, page AOWB1 Minimum variance control in presence of actuator saturation in adaptive optics Optimal control, observers and integrators in adaptive optics, Comptes rendus (Doklady) de l'Académie des Sciences Proc. of the SPIE, pp.301-305, 2006.

. Lane, Simulation of a Kolmogorov phase screen, Waves in Random and Complex Media, pp.209-224, 1992.
DOI : 10.1088/0959-7174/2/3/003

. Lavigne, . Véran, J. Lavigne, and J. Et-véran, Woofer-tweeter control in an adaptive optics system using a Fourier reconstructor, Journal of the Optical Society of America A, vol.25, issue.9, pp.252271-2279, 2008.
DOI : 10.1364/JOSAA.25.002271

M. Le-louarn, Multi-Conjugate Adaptive Optics with laser guide stars: performance in the infrared and visible, Monthly Notices of the Royal Astronomical Society, vol.334, issue.4, pp.865-874, 2002.
DOI : 10.1046/j.1365-8711.2002.05552.x

[. Roux and B. , Commande optimale en Optique Adaptative Classique et Multiconjuguée, p.162, 2003.

R. Le, Optimal control law for classical and multiconjugate adaptive optics, J. Opt. Soc. Am. A, vol.21, issue.119, pp.1261-1276, 2004.

L. H. Lee, Sparse-Matrix Regularization for Minimum-Variance Reconstruction of Pseudo-Kolmogorov Turbulence, Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, pp.2-145, 2007.
DOI : 10.1364/AOPT.2007.JTuA2

. Lessard, Experimental validation of single-iteration multigrid wavefront reconstruction at the Palomar Observatory, Optics Letters, vol.33, issue.18, pp.332047-2049, 2008.
DOI : 10.1364/OL.33.002047

D. P. Looze, Minimum variance control structure for adaptive optics systems, Journal of the Optical Society of America A, vol.23, issue.3, pp.603-612, 2006.
DOI : 10.1364/JOSAA.23.000603

D. P. Looze, Discrete-time model of an adaptive optics systems, Journal of the Optical Society of America A, vol.24, issue.9, pp.2850-169, 2007.
DOI : 10.1364/JOSAA.24.002850

D. P. Looze, Structure of a hybrid signal LQG controller for adaptive optics, Adaptive Optics Systems, p.107, 2008.
DOI : 10.1117/12.789116

D. P. Looze, Linear-quadratic-Gaussian control for adaptive optics systems using a hybrid model, Journal of the Optical Society of America A, vol.26, issue.1, pp.1-9, 2009.
DOI : 10.1364/JOSAA.26.000001

. Looze, Optimal Compensation and Implementation for Adaptive Optics Systems, Experimental Astronomy, vol.15, issue.2, pp.67-88, 2003.
DOI : 10.1023/B:EXPA.0000036150.62118.64

L. Et-tallon-]-louarn, M. L. Et-tallon, and M. , Analysis of modes and behavior of a multiconjugate adaptive optics system, Journal of the Optical Society of America A, vol.19, issue.5, pp.912-925, 2002.
DOI : 10.1364/JOSAA.19.000912

. Lundström, . Unsbo, L. Lundström, and P. Et-unsbo, Transformation of Zernike coefficients: scaled, translated, and rotated wavefronts with circular and elliptical pupils, Journal of the Optical Society of America A, vol.24, issue.3, 2007.
DOI : 10.1364/JOSAA.24.000569

D. G. Macmartin, Local, hierarchic, and iterative reconstructors for adaptive optics, Journal of the Optical Society of America A, vol.20, issue.6, pp.1084-1093, 2003.
DOI : 10.1364/JOSAA.20.001084

P. Madec, Adaptive Optics for Astronomy, chapter Control Techniques, p.46, 1999.

B. L. Mcglamery, Computer simulation studies of compensation of turbulence degraded images, Image Processing, issue.74, pp.2257-233, 1976.

S. Meimon, An optimized calibration strategy for high order adaptive optics systems : the Slope-Oriented Hadamard Actuation, Proc. of the AO4ELT Conference. EDP Sciences, p.58, 2009.

. Michau, Wavefront sensing from extended sources, Real Time and Post Facto Solar Image Correction, pp.124-128, 1992.
DOI : 10.1117/12.682728

. Montilla, Comparison of Reconstruction and Control algorithms on the ESO end-to-end simulator OCTOPUS, 1st AO4ELT conference, Adaptive Optics for Extremely Large Telescopes, p.127, 2009.
DOI : 10.1051/ao4elt/201003002

. Morari, . Zafiriou, M. Morari, and E. Et-zafiriou, Robust Process Control, p.125, 1989.

L. Mugnier, Des donnéesdonnées`donnéesà la connaissance de l'objet : leprobì eme inverse, p.56, 2008.

L. Mugnier, . Besnerais, L. Mugnier, and G. Et-le-besnerais, Probì emes inverses en imagerie optiquè a travers la turbulence, Approche bayésienne pour lesprobì emes inverses, chapter 10, pp.241-270, 2001.

. Neichel, Tomographic reconstruction for wide-field adaptive optics systems: Fourier domain analysis and fundamental limitations, Journal of the Optical Society of America A, vol.26, issue.1, pp.219-235, 2009.
DOI : 10.1364/JOSAA.26.000219

. Nicolle, Improving the Shack- Hartmann wave-front sensor measurement for extreme adaptive optics, Opt. Lett, issue.23, pp.292743-2745, 2004.

R. J. Noll, Zernike polynomials and atmospheric turbulence*, Journal of the Optical Society of America, vol.66, issue.3, pp.207-211, 1976.
DOI : 10.1364/JOSA.66.000207

. Oppenheim, . Schafer, A. V. Oppenheim, and R. W. Et-schafer, Discrete-time signal processing, p.64, 1999.

. Oppenheim, . Willsky, A. V. Oppenheim, and A. S. Et-willsky, Signals & Systems, p.64, 1997.

A. Papoulis, Systems and Transforms with Applications in Optics, p.97, 1968.

A. Papoulis, A new algorithm in spectral analysis and band-limited extrapolation, IEEE Transactions on Circuits and Systems, vol.22, issue.9, pp.735-742, 1975.
DOI : 10.1109/TCS.1975.1084118

. Paschall, Design of a linear quadratic Gaussian controller for an adaptive optics system, [1991] Proceedings of the 30th IEEE Conference on Decision and Control, pp.1761-1769, 1991.
DOI : 10.1109/CDC.1991.261709

R. Ragazzoni, Pupil plane wavefront sensing with an oscillating prism, Journal of Modern Optics, vol.11, issue.2, pp.289-293, 1996.
DOI : 10.1364/AO.14.001169

. Ragazzoni, Adaptive-optics corrections available for the whole sky, Nature, vol.450, issue.6765, pp.54-56, 2000.
DOI : 10.1038/47425

. Ramos, Fpga-based slope computation for elts adaptive optics wavefrontsensors Introduction to Stochastic Control Theory, Proc. of the SPIE series : Mathematics in science and engineering series, pp.701530-70, 1970.

. Raynaud, Minimum variance control of astronomical adaptive optics systems with actuator dynamics under synchronous and asynchonous sampling, J.-M. International Journal of Robust and Nonlinear Control, vol.174, issue.182, p.184, 2010.

. Rembe, Stroboscopic interferometer with variable magnification to measuredynamics in an adaptive-optics micromirror, IEEE/LEOS International, pp.73-74, 2000.

. Ren, Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm, Applied Optics, vol.44, issue.13, pp.2626-2637, 2005.
DOI : 10.1364/AO.44.002626

. Riccardi, The adaptive secondary mirrors for the Large Binocular Telescope: a progress report, Advancements in Adaptive Optics, pp.1564-1571, 2004.
DOI : 10.1117/12.551578

. Riccardi, The adaptive secondary mirror for the Large Binocular Telescope: results of acceptance laboratory test, Adaptive Optics Systems, p.40, 2008.
DOI : 10.1117/12.790527

R. Et-gendron-]-rigaut, F. Et-gendron, and E. , Laser guide star in adaptive optics -the tilt determination problem, Astronomy and Astrophysics, vol.261, pp.677-684, 1992.

. Rigaut, Analytical model for Shack-Hartmann-based adaptive optics systems, Adaptive Optical System Technologies, pp.1038-1048, 1998.
DOI : 10.1117/12.321649

. Rivera, Internal model control: PID controller design, Industrial & Engineering Chemistry Process Design and Development, vol.25, issue.1, pp.252-265, 1985.
DOI : 10.1021/i200032a041

F. Roddier, The effects of atmospherical turbulence in optical astronomy, volume XIX of Progress in Optics, pp.281-376, 1981.

F. Roddier, Adaptive Optics in Astronomy, pp.38-68, 1999.

. Roddier, One-dimensional spectra of turbulence-induced Zernike aberrations: time-delay and isoplanicity error in partial adaptive compensation, Journal of the Optical Society of America A, vol.10, issue.5, pp.957-965, 1993.
DOI : 10.1364/JOSAA.10.000957

R. Et-roddier-]-roddier, F. Et-roddier, and C. , Wavefront reconstruction using iterative Fourier transforms, Applied Optics, vol.30, issue.11, pp.1325-1327, 1991.
DOI : 10.1364/AO.30.001325

N. Roddier, Atmospheric wavefront simulation using Zernike polynomials, Optical Engineering, vol.29, issue.10, pp.1174-1180, 1990.
DOI : 10.1117/12.55712

R. Et-welch-]-roggemann, M. C. Welch, and B. , Imaging through turbulence, p.68, 1996.

T. S. Ross, Limitations and applicability of the Mar??chal approximation, Applied Optics, vol.48, issue.10, pp.1812-1818, 2009.
DOI : 10.1364/AO.48.001812

. Rousset, First diffraction-limited astronomical images with adaptive optics, Astronomy and Astrophysics, vol.230, issue.15, pp.29-32, 1990.

. Rousset, Status of the VLT Nasmyth adaptive optics system (NAOS), Proc. SPIE, pp.72-81, 2000.

Y. Saad, Iterative Methods for sparse linear systems, SIAM, vol.61, issue.149, pp.148-150, 1996.
DOI : 10.1137/1.9780898718003

. Schwartz, Turbulence-degraded wave fronts as fractal surfaces, Journal of the Optical Society of America A, vol.11, issue.1, pp.444-451, 1994.
DOI : 10.1364/JOSAA.11.000444

B. Sedghi, E-ELT Main Axis Control Analysis, Issue 3, p.205, 2007.

. Shi, Local wavefront reconstruction : Simulations, experiments and predictions, p.61, 2002.
DOI : 10.1117/12.457134
URL : https://trs.jpl.nasa.gov/bitstream/2014/37185/1/02-2150.pdf

T. Söderström, Discrete-time Stochastic Systems Advanced Textbooks in Control and Signal Processing, pp.114-173, 2002.

. Tallon, 3-D Wavefront Sensing for Multiconjugate Adaptive Optics, European Southern Observatory Astrophysics Symposia, pp.517-562, 1992.

. Tallon, A Fractal Iterative Method for Fast Wavefront Reconstruction for Extremely Large Telescopes, Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, pp.2-150, 2007.
DOI : 10.1364/AOPT.2007.PMA2

G. I. Taylor, The Spectrum of Turbulence, Proc. Royal Society of London Series A, pp.476-490, 1938.
DOI : 10.1098/rspa.1938.0032

. Thomas, Comparison of centroid computation algorithms in a Shack-Hartmann sensor, Monthly Notices of the Royal Astronomical Society, vol.371, issue.1, pp.323-336, 2006.
DOI : 10.1111/j.1365-2966.2006.10661.x

S. P. Timoshenko, Theory of Plates and Shells, 0193.

. Tokovinin, Isoplanatism in a multiconjugate adaptive optics system, Journal of the Optical Society of America A, vol.17, issue.10, pp.171819-1827, 2000.
DOI : 10.1364/JOSAA.17.001819

. Tokovinin, A. Viard-]-tokovinin, and E. Viard, Limiting precision of tomographic phase estimation, Journal of the Optical Society of America A, vol.18, issue.4, pp.873-882, 2001.
DOI : 10.1364/JOSAA.18.000873

I. Troch, Solving the discrete Lyapunov equation using the solution of the corresponding continuous Lyapunov equation and vice versa, IEEE Transactions on Automatic Control, vol.33, issue.10, pp.944-966, 1988.
DOI : 10.1109/9.7250

R. J. Vaccaro, Digital Control : A State-Space Approach. McGraw-Hill. 196 [van Loan Computing integrals involving the matrix exponential, IEEE Transactions on Automatic Contol, vol.23, issue.3, p.217, 1978.

. Véran, . Herriot, J. Véran, and G. Et-herriot, Woofer-tweeter tip-tilt control for NFIRAOS on TMT, Advances in Adaptive Optics II, p.208, 2006.
DOI : 10.1117/12.672446

C. Vérinaud, On the nature of the measurements provided by a pyramid wave-front sensor, Optics Communications, vol.233, issue.1-3, pp.27-38, 2004.
DOI : 10.1016/j.optcom.2004.01.038

. Vernet, The field stabilization and adaptive optics mirrors for the European Extremely Large Telescope, Proc. of the SPIE, pp.70150-210, 2008.

C. Vogel, Computational Methods for Inverse Problems, Society for Industrial & Applied Mathematics, p.149, 2002.
DOI : 10.1137/1.9780898717570

Y. Vogel, C. Vogel, and . Yang, Multigrid algorithm for least-squares wavefront reconstruction, Applied Optics, vol.45, issue.4, pp.705-715, 2004.
DOI : 10.1364/AO.45.000705

C. R. Vogel, Sparse matrix methods for wavefront reconstruction, revisited, Advancements in Adaptive Optics, pp.1327-1335, 2004.
DOI : 10.1117/12.548689
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.69.5971

J. S. Walker, A primer on Wavelets and their Scientific Applications, Studies in Advanced Mathematics. Chapman and Hall, p.61, 1999.
DOI : 10.1201/9781420050011

E. P. Wallner, Optimal wave-front correction using slope measurements, Journal of the Optical Society of America, vol.73, issue.12, pp.1771-1776, 1983.
DOI : 10.1364/JOSA.73.001771

W. Wang, J. Y. Et-markey, and J. K. , Modal compensation of atmospheric turbulence phase distortion*, Journal of the Optical Society of America, vol.68, issue.1, pp.78-87, 0194.
DOI : 10.1364/JOSA.68.000078

. Wiberg, A spatial non-dynamic LQG controller: Part I, application to adaptive optics, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), p.107, 1994.
DOI : 10.1109/CDC.2004.4607231

. Wiberg, A spatial non-dynamic LQG controller: Part II, theory, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), pp.3333-3338, 1994.
DOI : 10.1109/CDC.2004.1428998

N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, p.70, 1949.

H. S. Witsenhausen, Separation of estimation and control for discrete time systems, Proceedings of the IEEE, vol.59, issue.11, pp.1557-1971, 1971.
DOI : 10.1109/PROC.1971.8488

J. Wu, B. Wu, and E. Et-jonckheere, A simplified approach to Bode's theorem for continuous-time and discrete-time systems, IEEE Transactions on Automatic Control, vol.37, issue.11, pp.371797-1802, 1992.
DOI : 10.1109/9.173154

Y. Vogel, Q. Yang, and C. R. Vogel, Fourier domain algorithm for the fitting step in multi-conjugate adaptive optics, Proc. of the SPIE - Advances in Adaptive Optics II, pp.62722-142, 2006.

R. Zou, W. Zou, and J. P. Et-rolland, Quantifications of error propagation in slope-based wavefront estimations, Journal of the Optical Society of America A, vol.23, issue.10, pp.2629-2638, 2006.
DOI : 10.1364/JOSAA.23.002629