S. Wiggins and M. Golubitsky, Introduction to applied nonlinear dynamical systems and chaos, 1990.
DOI : 10.1007/978-1-4757-4067-7

T. Hull, W. Enright, B. Fellen, and A. Sedgwick, Comparing Numerical Methods for Ordinary Differential Equations, SIAM Journal on Numerical Analysis, vol.9, issue.4, pp.603-637, 1972.
DOI : 10.1137/0709052

J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, 1983.

F. Chinesta, P. Ladeveze, and E. Cueto, A Short Review on Model Order Reduction Based on Proper Generalized Decomposition, Archives of Computational Methods in Engineering, vol.69, issue.9, pp.395-404, 2011.
DOI : 10.1007/s11831-011-9064-7

URL : https://hal.archives-ouvertes.fr/hal-01004940

Y. Liang, H. Lee, S. Lim, W. Lin, K. Lee et al., PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS???PART I: THEORY, Journal of Sound and Vibration, vol.252, issue.3, pp.527-544, 2002.
DOI : 10.1006/jsvi.2001.4041

P. Dutta, A. Halder, and R. Bhattacharya, Nonlinear filtering with transfer operator, 2013 American Control Conference, pp.3069-3074, 2013.
DOI : 10.1109/ACC.2013.6580302

URL : https://hal.archives-ouvertes.fr/hal-00785159

P. Dutta and R. Bhattacharya, Nonlinear Estimation of Hypersonic State Trajectories in Bayesian Framework with Polynomial Chaos, Journal of Guidance, Control, and Dynamics, vol.33, issue.6, pp.1765-1778, 2010.
DOI : 10.2514/1.49743

E. Pruliere, F. Chinesta, and A. Ammar, On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition, Mathematics and Computers in Simulation, vol.81, issue.4, pp.791-810, 2010.
DOI : 10.1016/j.matcom.2010.07.015

URL : https://hal.archives-ouvertes.fr/hal-00704427

K. Takahashi, K. Yugi, K. Hashimoto, Y. Yamada, C. J. Pickett et al., Computational challenges in cell simulation: a software engineering approach, IEEE Intelligent Systems, vol.17, issue.5, pp.64-71, 2002.
DOI : 10.1109/MIS.2002.1039834

A. Nouy, A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.45-48, pp.4521-4537, 2007.
DOI : 10.1016/j.cma.2007.05.016

URL : https://hal.archives-ouvertes.fr/hal-00366619

M. Chevreuil and A. Nouy, Model order reduction based on proper generalized decomposition for the propagation of uncertainties in structural dynamics, International Journal for Numerical Methods in Engineering, vol.5, issue.2-4, pp.241-268, 2012.
DOI : 10.1002/nme.3249

URL : https://hal.archives-ouvertes.fr/hal-00603342

D. González, F. Masson, F. Poulhaon, A. Leygue, E. Cueto et al., Proper Generalized Decomposition based dynamic data driven inverse identification, Mathematics and Computers in Simulation, vol.82, issue.9, pp.1677-1695, 2012.
DOI : 10.1016/j.matcom.2012.04.001

C. Ghnatios, F. Masson, A. Huerta, A. Leygue, E. Cueto et al., Proper generalized decomposition based dynamic datadriven control of thermal processes, Computer Methods in Applied Mechanics and Engineering, vol.213, pp.29-41, 2012.

J. Fisher and R. Bhattacharya, Linear quadratic regulation of systems with stochastic parameter uncertainties, Automatica, vol.45, issue.12, pp.2831-2841, 2009.
DOI : 10.1016/j.automatica.2009.10.001

F. Chinesta, A. Ammar, and E. Cueto, Recent Advances and New Challenges in the Use of the Proper Generalized Decomposition for Solving Multidimensional Models, Archives of Computational Methods in Engineering, vol.190, issue.1, pp.327-350, 2010.
DOI : 10.1007/s11831-010-9049-y

URL : https://hal.archives-ouvertes.fr/hal-01007235

J. Brewer, Kronecker products and matrix calculus in system theory, IEEE Transactions on Circuits and Systems, vol.25, issue.9, pp.772-781, 1978.
DOI : 10.1109/TCS.1978.1084534

A. E. Bryson, Applied Optimal Control: Optimization, Estimation, and Control, IEEE Transactions on Systems, Man, and Cybernetics, vol.9, issue.6, 1975.
DOI : 10.1109/TSMC.1979.4310229

A. Nouy, Generalized spectral decomposition method for solving stochastic finite element equations: Invariant subspace problem and dedicated algorithms, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.51-52, pp.4718-4736, 2008.
DOI : 10.1016/j.cma.2008.06.012

URL : https://hal.archives-ouvertes.fr/hal-00366613

J. W. Daniel, W. B. Gragg, L. Kaufman, and G. Stewart, Reorthogonalization and stable algorithms for updating the Gram-Schmidt factorization Numerics of Gram-Schmidt orthogonalization, Mathematics of Computation Linear Algebra and Its Applications, vol.30, issue.197, pp.772-795, 1976.

A. Young, C. Cao, N. Hovakimyan, and E. Lavretsky, An Adaptive Approach to Nonaffine Control Design for Aircraft Applications, AIAA Guidance, Navigation, and Control Conference and Exhibit, pp.2006-6343, 2006.
DOI : 10.2514/6.2006-6343

A. Falcó and A. Nouy, Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces, Numerische Mathematik, vol.115, issue.45???48, pp.503-530, 2012.
DOI : 10.1007/s00211-011-0437-5