Title page for ETD etd-04282004-164740


Type of Document Dissertation
Author Vugrin, Eric D.
Author's Email Address evugrin@vt.edu
URN etd-04282004-164740
Title On Approximation and Optimal Control of Nonnormal Distributed Parameter Systems
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Burns, John A. Committee Chair
Borggaard, Jeffrey T. Committee Member
Cliff, Eugene M. Committee Member
Herdman, Terry L. Committee Member
Rogers, Robert C. Committee Member
Keywords
  • convection-diffusion equation
  • nonnormal
  • linear quadratic regulator problems
Date of Defense 2004-04-26
Availability unrestricted
Abstract
For more than 100 years, the Navier-Stokes equations and various linearizations have been used as a model to study fluid dynamics. Recently, attention has been directed toward studying the nonnormality of linearized problems and developing convergent numerical schemes for simulation of these sytems. Numerical schemes for optimal control problems often require additional properties that may not be necessary for simulation; these properties can be critical when studying nonnormal problems. This research is concerned with approximating infinite dimensional optimal control problems with nonnormal system operators.

We examine three different finite element methods for a specific convection-diffusion equation and prove convergence of the infinitesimal generators. Additionally, for two of these schemes, we prove convergence of the associated feedback gains. We apply these three schemes to control problems and compare the performance of all three methods.

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