Optimal boundary feedback flow stabilization by model reduction

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 25-28, 2007, Pages 2555-2569

  Ravindran, S S ^a  

^a UNIVERSITY OF ALABAMA IN HUNTSVILLE   (United States)

Author keywords

49K20; 65M60; 76D55; 76W05; Boundary feedback control; Nonlinear model reduction; Proper orthogonal decomposition; Singular value decomposition; Stabilization

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; FEEDBACK CONTROL; FLOW CONTROL; FLOW OF FLUIDS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; SINGULAR VALUE DECOMPOSITION;

BOUNDARY FEEDBACK CONTROL; FLOW STABILIZATION; NONLINEAR MODEL REDUCTION; PROPER ORTHOGONAL DECOMPOSITION;

AIRFOILS;

AIRFOILS; CLOSED LOOP CONTROL SYSTEMS; FEEDBACK CONTROL; FLOW CONTROL; FLOW OF FLUIDS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; SINGULAR VALUE DECOMPOSITION;

EID: 34147178122     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.11.026     Document Type: Article

References (34)

1. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, LAPACK Users' Guide, SIAM, Philadelphia, 1992. http://www.netlib.org/lapack/.
2. Brian Anderson D.O., and Moore J.B. Optimal Control: Linear Quadratic Methods (1990), Prentice-Hall, New Jersey
3. ∞-control theory of fluid dynamics. Roy. Soc. London Proc., Ser. A: Math. Engrg. Sci. 454 (1998) 3009-3033
4. Bensoussan A., Da Prato G., Delfour M., and Mitter S. Representation and Control of Infinite Dimensional Systems (1993), Birkhouser, Boston
5. Demmel J.W., and Kahan W.H. Accurate singular values of bidiagonal matrices. SIAM J. Sci. Comput. 11 (1990) 873-912
6. Fattorini H.O., and Sritharan S.S. Existence of optimal controls for viscous flow problems. Proc. Roy. Soc. London, Ser. A 439 (1992) 81-102
7. Gunzburger M.D. Perspectives in Flow Control and Optimization (2003), SIAM, Philadelphia
8. A.A. Hassan, D.D. JanakiRam, Effects of zero-mass synthetic jets on the aerodynamics of the NACA-0012 Airfoil, AIAA 97-2326, 1997.
9. Hilai R., and Rubinstein J. Recognition of rotated images by invariant Karhunen-Loeve expansion. J. Opt. Soc. Am. A - Opt. Image Sci. Vis. 11 (1994) 1610-1618
10. P. Holmes, J. Lumley, G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge, 1996.
11. Hou L.S., and Ravindran S.S. Computations of boundary optimal control problems for an electrically conducting fluid. J. Comput. Phys. 128 (1996) 319-330
12. Hou L.S., and Ravindran S.S. Numerical approximation of optimal flow control problems by a penalty method: error estimates and numerical results. SIAM J. Sci. Comput. 20 (1999) 1753-1777
13. Hou L.S., and Ravindran S.S. A penalized Neumann control approach for solving an optimal Dirichlet control problem for the Navier-Stokes equations. SIAM J. Control Optimization 36 (1997) 1795-1814
14. Ito K., and Ravindran S.S. Optimal control of thermally convected fluid flows. SIAM J. Sci. Comput. 19 (1998) 1847-1869
15. Ito K., and Ravindran S.S. A reduced order method for simulation and control of fluid flows. J. Comput. Phys. 143 (1998) 403-425
16. Karhunen K. Zur Spekraltheorie Stochasticher. Ann. Acad. Sci. Fennicae Ser. A 1 (1946) 34
17. Kailath T. Linear Systems (1980), Prentice-Hall
18. Kirby M., and Sirovich L. Application of the Karhunen-Loeve procedure for the characterization of human faces. IEEE Trans. Pattern Anal. Mach. Intell. 12 (1990) 103-108
19. Laub A.J. A schur method for solving algebraic Riccati equations. IEEE Trans. Automat. Control AC-24 (1979) 913-921
20. M. Loeve, Probability Theory, New York, 1955.
21. Lumley J.L. The structure of inhomogeneous turbulent flows. In: Yaglom A.M., and Tatarski V.I. (Eds). Atmospheric Turbulence and Radio Wave Propagation (1967), Nauka, Moscow 167-178
22. Ly H.V., and Tran H.T. Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor. Quart. Appl. Math. 60 (2002) 631-656
23. D.V. Maddalon, F.S. Collier, F.S. Montoya, C.K. Land, Transition flight experiments on a swept wing with suction, AIAA Paper 89-1893, 1989.
24. Modi V.J., Mokhtarian F., Fernando M., and Yokomizo T. Moving surface boundary-layer control as applied to two-dimensional airfoils. J. Aircraft 28 (1991) 104-112
25. Potter J.E. Matrix quadratic solutions. SIAM J. Appl. Math. 14 (1966) 496-501
26. Rajaee M., Karlsson S.K.F., and Sirovich L. Low-dimensional description of free shear flow coherent structures and their dynamical behavior. J. Fluid Mech. 258 (1994) 1-29
27. Ravindran S.S. A reduced order approach to optimal control of fluids using proper orthogonal decomposition. Int. J. Numer. Methods Fluids 34 (2000) 425-448
28. Ravindran S.S. Reduced-order adaptive controllers for fluid flows using POD. J. Sci. Comput. 15 (2000) 457-478
29. Ravindran S.S. Stabilization of Navier-Stokes equations by boundary feedback. Int. J. Numer. Anal. Model. 4 (2007)
30. S.S. Ravindran, Proper orthogonal decomposition in optimal control of fluids, NASA Technical Memorandum, NASA TM 1999-209113, 1999.
31. Ravindran S.S. Numerical approximation of optimal flow control problems by SQP method. In: Sritharan S.S. (Ed). Optimal Control of Viscous Flows, SIAM Proceedings in Applied Mathematics (1998), SIAM, Philadelphia 181-198
32. Sirovich L. Turbulence and the dynamics of coherent structures: Part I-III. Quart. Appl. Math. 45 (1987) 561-590
33. In: Sritharan S.S. (Ed). Optimal Control of Viscous Flows (1998), SIAM, Philadelphia
34. H. Yoshihara, D. Zonars, The transonic jet flap - a review of recent results, in: Proceedings, SAE National Aerospace & Manufacturing Meeting, 1975.