Type of Document Master's Thesis Author Flagg, Garret Michael Author's Email Address garretf@vt.edu URN etd-05222009-124513 Title An Interpolation-Based Approach to Optimal H∞ Model Reduction Degree Master of Science Department Mathematics Advisory Committee
Advisor Name Title Gugercin, Serkan Committee Chair Beattie, Christopher A. Committee Member Borggaard, Jeffrey T. Committee Member Keywords
- Model Reduction
- Rational Interpolation
- Optimization
Date of Defense 2009-05-05 Availability unrestricted Abstract A model reduction technique that is optimal in the H∞-norm has long been pursued dueto its theoretical and practical importance. We consider the optimal H∞ model reduction
problem broadly from an interpolation-based approach, and give a method for finding the
approximation to a state-space symmetric dynamical system which is optimal over a family
of interpolants to the full order system. This family of interpolants has a simple parameterization
that simplifi es a direct search for the optimal interpolant. Several numerical
examples show that the interpolation points satisfying the Meier-Luenberger conditions for
H_2 -optimal approximations are a good starting point for minimizing the H∞-norm of the
approximation error. Interpolation points satisfying the Meier-Luenberger conditions can
be computed iteratively using the IRKA algorithm [12]. We consider the special case of
state-space symmetric systems and show that simple sufficient conditions can be derived
for minimizing the approximation error when starting from the interpolation points found
by the IRKA algorithm. We then explore the relationship between potential theory in the
complex plane and the optimal H∞-norm interpolation points through several numerical experiments.
The results of these experiments suggest that the optimal H_2 approximation of
order r yields an error system for which significant pole-zero cancellation occurs, effectively
reducing an order n+r error system to an order 2r+1 system. These observations lead to a
heuristic method for choosing interpolation points that involves solving a rational Zolatarev
problem over a discrete set of points in the complex plane.
Files
Filename Size Approximate Download Time (Hours:Minutes:Seconds)
28.8 Modem 56K Modem ISDN (64 Kb) ISDN (128 Kb) Higher-speed Access mastersthesis.pdf 665.84 Kb 00:03:04 00:01:35 00:01:23 00:00:41 00:00:03
|
|
If you have questions or technical problems, please Contact DLA.
