Title page for ETD etd-05032012-141857


Type of Document Dissertation
Author Flagg, Garret Michael
Author's Email Address garretf@vt.edu
URN etd-05032012-141857
Title Interpolation Methods for the Model Reduction of Bilinear Systems
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Gugercin, Serkan Committee Chair
Ball, Joseph A. Committee Member
Beattie, Christopher A. Committee Member
Borggaard, Jeffrey T. Committee Member
Keywords
  • Optimization
  • Model Reduction
  • Nonlinear systems
  • Interpolation theory
  • Rational Krylov subspace methods
Date of Defense 2012-04-30
Availability unrestricted
Abstract
Bilinear systems are a class of nonlinear dynamical systems that arise in a variety of applications. In order to obtain a sufficiently accurate representation of the underlying physical phenomenon, these models frequently have state-spaces of very large dimension, resulting in the need for model reduction. In this work, we introduce two new methods for the model reduction of bilinear systems in an interpolation framework. Our first approach is to construct reduced models that satisfy multipoint interpolation constraints defined on the Volterra kernels of the full model. We show that this approach can be used to develop an asymptotically optimal solution to the H_2 model reduction problem for bilinear systems. In our second approach, we construct a solution to a bilinear system realization problem posed in terms of constructing a bilinear realization whose kth-order transfer functions satisfy interpolation conditions in k complex variables. The solution to this realization problem can be used to construct a bilinear system realization directly from sampling data on the kth-order transfer functions, without requiring the formation of the realization matrices for the full bilinear system.
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