Masters Theses
Date of Award
12-2010
Degree Type
Thesis
Degree Name
Master of Science
Major
Electrical Engineering
Major Professor
Seddik Djouadi
Committee Members
J. Douglas Birdwell, James J. Nutaro
Abstract
Model reduction is a powerful and ubiquitous tool used to reduce the complexity of a dynamical system while preserving the input-output behavior. It has been applied throughout many different disciplines, including controls, fluid and structural dynamics. Model reduction via proper orthogonal decomposition (POD) is utilized for of control of partial differential equations. In this thesis, the analytical expressions of POD modes are derived for the heat equation. The autocorrelation function of the latter is viewed as the kernel of a self adjoint compact operator, and the POD modes and corresponding eigenvalues are computed by solving homogeneous integral equations of the second kind. The computed POD modes are compared to the modes obtained from snapshots for both the one-dimensional and two-dimensional heat equation. Boundary feedback control is obtained through reduced-order POD models of the heat equation and the effectiveness of reduced-order control is compared to the full-order control. Moreover, the explicit computation of the POD modes and eigenvalues are shown to allow the computation of different n-widths approximations for the heat equation, including the linear, Kolmogorov, Gelfand, and Bernstein n-widths.
Recommended Citation
Fernandez, Tasha N., "Analytical Computation of Proper Orthogonal Decomposition Modes and n-Width Approximations for the Heat Equation with Boundary Control. " Master's Thesis, University of Tennessee, 2010.
https://trace.tennessee.edu/utk_gradthes/794
Included in
Controls and Control Theory Commons, Dynamic Systems Commons, Fluid Dynamics Commons, Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons, Partial Differential Equations Commons