Award#0325081 - ITR/AP: Collaborative Research: Model Reduction of Dynamical Systems for Real-time Control

Award Abstract #0325081

ITR/AP: Collaborative Research: Model Reduction of Dynamical Systems for Real-time Control

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.

P. Kloucek, D.C. Sorensen and J.L. Wightman. "The Approximation and Computation of a Basis of the Trace Space H-1/2," Journal of Scientific Computing, v.32 (1), 2007, p. 73.

P. Kloucek, D.C. Sorensen and J.L. Wightman. "The Approximation and Computation of a Basis of the Trace Space H-1/2," SIAM Journal on Scientific Computing, v.32 (, 2007.

Q. Zhou, K. Mohanram, and A.C. Antoulas. "Structure Preserving Reduction of Frequency-dependent Interconnect," Proceedings of the Design and Automation Conference (DAC), 2005, p. 939.

Q. Zhou, K. Sun, K. Mohanram, and D.C. Sorensen. "Large power grid analysis using domain decomosition," Procceeding of the Conference on Design Automation and Test in Europe, 2006, p. 27.

S. Gugercin and A.C. Antoulas. "Model reduction of large-scale systems by least squares," Linear Algebra and Applications, Special Issue on Order Reduction of Large-Scale Systems, Edited by P. Benner, D.C. Sorensen, R. Freund, and A. Varga, v.415, 2006, p. 290.

S. Gugercin and A.C. Antoulas. "An overview of balancing related model reduction methods and some new results," Int. Journal of Control, v.77, 2004, p. 748.

S. Gugercin, C. Beattie, E. Gildin, and A.C. Antoulas. "Controller reduction for large-scale systems," Proceedings of MTNS2004 (Mathematical Theory of Networks and Systems, Leuven, Belgium), v.1, 2004, p. 1.

S. Kundu, D.C. Sorensen, G.N. Phillips, Jr.. "Automatic Domain Decomposition of Proteins by a Gaussian Network Model," PROTEINS: Structure, Function, and Bioinformatics, v.57 (4), 2004, p. 725.