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Award Abstract #0324944
ITR/AP: Collaborative Research: Model Reduction of Dynamical Systems for Real Time Control
| NSF Org: |
CCF
Division of Computer and Communication Foundations
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| Initial Amendment Date: |
August 21, 2003 |
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| Latest Amendment Date: |
August 2, 2006 |
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| Award Number: |
0324944 |
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| Award Instrument: |
Continuing grant |
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| Program Manager: |
Almadena Y. Chtchelkanova
CCF Division of Computer and Communication Foundations
CSE Directorate for Computer & Information Science & Engineering
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| Start Date: |
September 1, 2003 |
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| Expires: |
August 31, 2008 (Estimated) |
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| Awarded Amount to Date: |
$414538 |
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| Investigator(s): |
Kyle Gallivan kgallivan@fsu.edu (Principal Investigator)
Paul Van Dooren (Co-Principal Investigator)
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| Sponsor: |
Florida State University
874 Traditions Way, 3rd Floor
TALLAHASSEE, FL 32306 850/644-5260
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| NSF Program(s): |
ITR MEDIUM (GROUP) GRANTS
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| Field Application(s): |
0000099 Other Applications NEC
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| Program Reference Code(s): |
HPCC, 9216, 1652
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| Program Element Code(s): |
1687
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ABSTRACT
This project proposes to extend the methods we have developed for model reduction of large-scale Linear Time Invariant (LTI) systems to a new regime of problems that require adaptive models. In particular, we will consider large-scale structured problems that are either time-varying, or which require adaptive updating of the initial reduced models to obtain better approximation properties.
Intellectual Merit
The research proposed here will provide efficient and robust methods for producing reduced order models of large state-space systems. This activity is expected to have an impact on system theory of complex systems, parallel numerical linear algebra for large-scale problems, and on efficient implementation of these schemes on parallel and distributed platforms. Once the theory and computational methods are developed, we expect that high quality software will result and have applications in many areas of engineering. This will enable the design of real time controllers for complex systems. This project will also have an impact on the education of students in computational science and engineering, both at the undergraduate and the graduate levels.
Broader Impact
The proposed project leverages extensively the existing intellectual and equipment infrastructure at Purdue, Rice, and Florida State Universities, as well as the Catholic University of Louvain, Belgium. The overall group of PI's and senior personnel bring extensive expertise and experience in dynamical systems, model reduction, control theory, seismic design and analysis of structures, numerical linear algebra, geometric modeling, data analysis and visualization, and parallel computing. In fact, collectively, they have had experience in designing and implementing numerical linear algebra algorithms on most of the significant high-performance commercial architectures and many of the experimental parallel architectures since the Illiac IV (designed and built in the late 1960's!). The three groups complement one another perfectly and are well-poised to successfully realize the goals of this proposal.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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(Showing: 1 - 10 of 27)
(Showing: 1 - 27 of 27)
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A. Vandendorpe and P. Van Doooren. "Model Reduction via Projection of Generalized State Space Systems," Proceedings IEEE 2005 Conference on Decision and Control, 2005, p. 6557.
A. Vandendorpe, P.~Van Dooren. "Model reduction of
interconnected systems," Proceedings 2004 International Symposium Math. Th. Netw.
Syst., Leuven, Belgium, 2004, p. on CD.
A. Vandendorpe, P.~Van Dooren. "Model reduction of," Proceedings 2004 International Symposium Math. Th. Netw., 2004, p. on CD.
A.~Antoulas, D.~Sorensen, K.~Gallivan, P.~Van Dooren,A.~Grama, C.~Hoffmann, A.~Sameh. "Model reduction of large-scale
dynamical systems," Lecture Notes in Computer Science, Proceedings 2004 International Conference on
Computational Science, Springer Verlag, v.3038, 2004, p. 740.
A.~Antoulas, D.~Sorensen, K.~Gallivan, P.~Van Dooren,A.~Grama, C.~Hoffmann, A.~Sameh. "Model reduction of large-scale," Lecture Notes in Computer Science, Proceedings 2004 International Conference on, v.3038, 2004, p. 740.
C.G. Baker, P.-A. Absil, and K.A. Gallivan. "An Implicit Riemannian Trust-Region Method for the Symmetric Generalized Eigenproblem," Lecture Notes in Computational Science -- Proceedings of ICCS 2006, v.3991, 2006, p. 210.
Christopher G. Baker, Pierre-Antoine Absil, Kyle A. Gallivan. "An implicit trust-region method on Riemannian manifolds," IMA Journal of Numerical Analysis, v.28, 2008, p. 665.
D. Bouagada and P. Van Dooren. "Stability margins for generalized state space systems," Applied Mathematics Letters, v.19, 2006, p. 451.
D. Lemonnier and P. Van Dooren. "Balancing Regular Matrix Pencils," SIAM Journal on Matrix Analysis and Applications, v.28, 2006, p. 253.
K. A. Gallivan, A. Vandendorpe, and P. Van Dooren. "Sylvester Equations and Model Reduction," Proceedings 2006 International Symposium on Mathematical Theory of Networks and Systems, 2006, p. on CD.
K. Gallivan, X. Rao, and P. Van Dooren. "Singular Riccati Equations Stabilizing Large-scale Systems.," Linear Algebra and Its Applications, v.415, 2006, p. 359.
M. Overton and P. Van Dooren,. "On computing the complex passivity radius," Proceedings IEEE 2005 Conference on Decision and Control, 2005, p. 7960.
P. Van Dooren, K. A. Gallivan, and P.-A. Absil. "H2-optimal Model Reduction of MIMO Systems," Applied Mathematics Letters, v.21, 2008, p. 1267.
P.-A. Absil and K. A. Gallivan. "Joint Diagonalization on the Oblique Manifold for Independent Component Analysis," Proceedings of IEEE 2006 International Conferance on Acoustics, Speech and Signal Processing.
, 2006, p. on CD.
P.-A. Absil, C. G. Baker, and K. A. Gallivan. "Trust-region Algorithms for the Generalized Symmetric Eigenvalue Problem," Journal of Computational and Applied Mathematics, v.189, 2006, p. 274.
P.-A. Absil, C. G. Baker, and K. A. Gallivan. "Trust-region Algorithms for the Generalized Symmetric Eigenvalue Problem," Journal of Computational and Applied Mathematics, v.189, 2006, p. 274.
P.-A. Absil, C. G. Baker, and K. A. Gallivan. "Trust-region Methods on Riemannian Manifolds," Foundations of Computational Mathematics, v.7, 2007, p. 303.
P.-A. Absil, C. G. Baker, and K. A. Gallivan. "Trust-region Methods on Riemannian Manifolds with Applications in Numerical Linear," Proceedings of 2004 International Symposium on Mathematical Theory of Networks and, 2004, p. on CD.
P.-A. Absil, R. Mahony, and R. Sepulchre. "Continuous-time subspace flows related to the symmetric eigenvalue problem," Pacific Journal of Optimization, v.4, 2008, p. 179.
P.A. Absil, C. G. Baker, K. A. Gallivan and A. Sameh. "Adaptive model trust region methods for generalized eigenvalue problems," Proceedings of 2005 International Conference on Computational Science Part I,
Lecture Notes in Computer Science No. 3514, Springer-Verlag, Vaidy S. Sunderam et al.
Eds., v.3514, 2005, p. 33.
P.A. Absil, C. G. Baker, K. A. Gallivan and A. Sameh. "Adaptive model trust region methods for generalized eigenvalue problems," Proceedings of 2005 International Conference on Computational Science Part I,, v.3514, 2005, p. 33.
Y. Chahlaoui, K. A. Gallivan, and P. Van Dooren. "Calculating the H-infinity-norm of Large Sparse Systems via Chandrasekhar Iterations and Extrapolation," European Series in Applied and Industrial Mathematics Proceedings, v.20, 2007, p. 83.
Y. Chahlaoui, K.~Gallivan, P.~Van Dooren. "$H_{\infty}$-norm calculation for large sparse systems," Proceedings of 2004 International Symposium Math. Th. Netw. Syst., Leuven, Belgium, 2004, p. on CD.
Y. Chahlaoui, K.~Gallivan, P.~Van Dooren. "$H_{\infty}$-norm calculation for large sparse systems," Proceedings of 2004 International Symposium Math. Th. Netw. Syst., Leuven, Belgium, 2004, p. on CD.
Y. Wu, X. Liu, W. Mio and K. Gallivan. "Two-stage Optimal Component Analysis via Dimensional Reduction," Computer Vision and Image Understanding, v.10, 2008, p. 91.
Y. Wu, X. Liu, W. Mio, and K. A. Gallivan. "Two-stage Optimal Component Analysis," Proceedings 2006 2006 International Conference on Image Processing, 2006, p. 1652.
Y.~Chahlaoui, D.~Lemonnier, A.~Vandendorpe, P.~Van Dooren,. "Second-order structure preserving model reduction," Proceedings 2004 International Symposium Math. Th. Netw. Syst., Leuven, Belgium,, 2004.
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