NDLI: On a generalization of the proper orthogonal decomposition and optimal construction of reduced order models

Content Provider	IEEE Xplore Digital Library
Author	Djouadi, S.M. Sahyoun, S.
Copyright Year	2012
Description	Author affiliation: Dept. of Electr. Eng. & Comput. Sci., Univ. of Tennessee, Knoxville, TN, USA (Djouadi, S.M.; Sahyoun, S.)
Abstract	In this paper, the popular proper orthogonal decomposition (POD) without the usual integral or inner product constraints is extended to general Hilbert spaces, such as Sobolev spaces, using functional analytic methods. It is shown that a particular tensor product space is dense in the Hilbert space where the partial differential equation (PDE) solution lives. This allows approximating the PDE solution by tensors to any desired accuracy. Optimal approximation by these tensors is shown to result in the POD using operator theoretic arguments. This is achieved by solving a nonlinear optimization problem where the PDE solution is approximated by operators of a prescribed finite rank in the corresponding trace class 2 norm. POD modes can then be computed by solving an infinite dimensional eigenvalue problem using Hilbert-Schmidt theory. Moreover, an optimal method in constructing reduced order models for the two-dimensional Burgers' equation subject to boundary control is presented and compared to the POD reduced models. A closed-loop feedback controller then designed using the reduced order model and then applied to the full order model.
Sponsorship	IEEE Control Syst. Soc.
Starting Page	1436
Ending Page	1441
File Size	1166314
Page Count	6
File Format	PDF
ISBN	9781457710957
ISSN	07431619
e-ISBN	9781457710964
e-ISBN	9781467321020
DOI	10.1109/ACC.2012.6315479
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-06-27
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Boundary conditions Reduced order systems Hilbert space Tensile stress Approximation methods Eigenvalues and eigenfunctions Optimization
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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