POD Model Reduction with Stability Guarantee

Proceedings of the IEEE Conference on Decision and Control

Volumn 5, Issue , 2003, Pages 5254-5258

  Prajna, Stephen ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CORRELATION METHODS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; OPTIMIZATION; PERTURBATION TECHNIQUES; STABILITY; THEOREM PROVING;

DYNAMIC MODELS; PROPER ORTHOGONAL DECOMPOSITION (POD);

CONTROL SYSTEMS;

EID: 1542289893     PISSN: 01912216     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (13)

1. A. C. Antoulas, D. C. Sorensen, and S. Gugercin. A survey of model reduction methods for large-scale systems. In Structured Matrices in Mathematics, Computer Science, and Engineering, pages 193-219. American Mathematical Society, Providence, RI, 2001.
2. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics (SIAM), 1994.
3. G. E. Dullerud and F. Paganini. A Course in Robust Control Theory: A Convex Approach. Springer-Verlag NY, 2000.
4. P. Holmes, J. L. Lumley, and G. Berkooz. Turbulence, Coherent Structures, Dynamical Systems, and Symmetry. Cambridge University Press, 1996.
5. R. A. Horn and C. R. Johnson. Topics in Matrix Analysis. Cambridge University Press, 1991.
6. H. Hotelling. Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24:417-441,498-520, 1933.
7. S. Lall, J. E. Marsden, and S. Glavaski. A subspace approach to balanced truncation for model reduction of nonlinear control systems. International Journal on Robust and Nonlinear Control, 12(5):519-535, 2002.
8. M. Loève. Probability Theory: Foundations, Random Sequences. D. Van Nostrand Company, Inc., 1955.
9. J. L. Lumley. The structure of inhomogeneous turbulence. In Atmospheric Turbulence and Wave Propagation, pages 166-178. Nauka, Moscow, 1967.
10. M. Rathinam and L. R. Petzold. A new look at proper orthogonal decomposition. Submitted to SIAM Journal on Numerical Analysis, 2002.
11. C. W. Rowley. Personal communication. 2003.
12. C. W. Rowley, T. Colonius, and R. M. Murray. Model reduction for compressible flows using POD and Galerkin projection. Submitted to Physica D, 2002.
13. J. F. Sturm. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 11-12:625-653, 1999. Available at http://fewcal.kub.nl/sturm/software/sedumi.html.