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ESAIM: M2AN
Volume 42, Number 1, January-February 2008
Page(s) 1 - 23
DOI http://dx.doi.org/10.1051/m2an:2007054
Published online 12 January 2008
  1. K. Afanasiev and M. Hinze, Adaptive control of a wake flow using proper orthogonal decomposition, in Lecture Notes in Pure and Applied Mathematics 216, Marcel Dekker (2001) 317–332.
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  3. P. Astrid, S. Weiland, K. Willcox and T. Backx, Missing point estimation in models described by proper orthogonal decomposition, in 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas (2004).
  4. H.T. Banks, M.L. Joyner, B. Winchesky and W.P. Winfree, Nondestructive evaluation using a reduced-order computational methodology. Inverse Problems 16 (2000) 1–17.
  5. G. Berkooz, P. Holmes and J.L. Lumley, Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge Monographs on Mechanics, Cambridge University Press (1996).
  6. P. Constantin and C.Foias, Navier-Stokes Equations. Chicago Lectures in Mathematics, University of Chicago Press, Chicago (1989).
  7. M.A. Grepl and A.T. Patera, A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. ESAIM: M2AN 39 (2005) 157–181. [CrossRef] [EDP Sciences]
  8. S. Gugercin and A.C. Antoulas, A survey of model reduction by balanced truncation and some new results. Int. J. Control 77 (2004) 748–766. [CrossRef]
  9. T. Henri, Réduction de modéles par des méthodes de décomposition orthogonal propre. Ph.D. thesis, Université de Rennes, France (2004).
  10. C. Homescu, L.R. Petzold and R. Serban, Error estimation for reduced order models of dynamical systems. SIAM J. Numer. Anal. 43 (2005) 1693–1714. [CrossRef] [MathSciNet]
  11. K. Ito and S.S. Ravindran, Reduced basis method for unsteady viscous flows. Int. J. Comp. Fluid Dynam. 15 (2001) 97–113. [CrossRef] [MathSciNet]
  12. K. Kunisch and S. Volkwein, Control of Burgers' equation by a reduced order approach using proper orthogonal decomposition. J. Optim. Theor. Appl. 102 (1999) 345–371. [CrossRef] [MathSciNet]
  13. K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM J. Numer. Anal. 40 (2002) 92–515.
  14. K. Kunisch, S. Volkwein and L. Xie, HJB-POD based feedback design for the optimal control of evolution problems. SIAM J. Appl. Dynam. Syst. 4 (2004) 701–722. [CrossRef]
  15. S. Lall, J.E. Marsden and S. Glavaški, A subspace approach to balanced truncation for model reduction of nonlinear control systems. Int. J. Robust Nonlinear Control 12 (2002) 519–535. [CrossRef]
  16. H.V. Ly and H.T. Tran, Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor. Quarterly Appl. Math. 60 (2002) 631–656.
  17. H. Maurer and J. Zowe, First and second order necessary and sufficient optimality conditions for infinite-dimensional programming problems. Math. Programming 16 (1979) 98–110. [CrossRef] [MathSciNet]
  18. B.C. Moore, Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Automatic Control AC-26 (1981) 17–31.
  19. S.S. Ravindran, Adaptive reduced-order controllers for a thermal flow system using proper orthogonal decomposition. SIAM J. Sci. Comput. 23 (2002) 1924–1942. [CrossRef] [MathSciNet]
  20. D.V. Rovas, L. Machiels and Y. Maday, Reduced-basis output bound methods for parabolic problems. IMA J. Numer. Anal. 26 (2006) 423–445. [CrossRef] [MathSciNet]
  21. C.W. Rowley, Model reduction for fluids using balanced proper orthogonal decomposition. Int. J. Bifurcation Chaos 15 (2005) 997–1013. [CrossRef]
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  23. K.Y. Tan, W.R. Graham and J. Peraire, Active flow control using a reduced order model and optimum control. AIAA (1996).
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  25. S. Volkwein, Second-order conditions for boundary control problems of the Burgers equation. Control Cybern. 30 (2001) 249–278.
  26. S. Volkwein, Boundary control of the Burgers equation: optimality conditions and reduced-order approach, in Optimal Control of Complex Structures, K.-H. Hoffmann, I. Lasiecka, G. Leugering, J. Sprekels and F. Tröltzsch Eds., International Series of Numerical Mathematics 139 (2001) 267–278.
  27. S. Volkwein, Lagrange-SQP techniques for the control constrained optimal boundary control problems for the Burgers equation. Comput. Optim. Appl. 26 (2003) 253–284. [CrossRef] [MathSciNet]
  28. K. Willcox and J. Peraire, Balanced model reduction via the proper orthogonal decomposition, in 15th AIAA Computational Fluid Dynamics Conference, Anaheim, USA (June 2001).

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