Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations

Proper Orthogonal Decomposition for Reduced Basis Feedback Controllers for Parabolic Equations

In this paper, we present a discussion of the proper orthogonal decomposition (POD) as applied to simulation and feedback control of the one dimensional heat equation. We provide two examples of input collections to which the POD process is applied. First, we apply POD directly to the nite element basis of linear B-splines. Next we additionally include time snapshots. We show that although the ...

Proper Orthogonal Decomposition for Reduced Order Feedback Control of Partial Differential Equations

Isogeometric analysis and proper orthogonal decomposition for parabolic problems

We investigate the combination of Isogeometric Analysis (IGA) and proper orthogonal decomposition (POD) based on the Galerkin method for model order reduction of linear parabolic partial differential equations. For the proposed fully discrete scheme, the associated numerical error features three components due to spatial discretization by IGA, time discertization with the θ -scheme, and eigenva...

Reduced Order Controllers for Spatially Distributed Systems via Proper Orthogonal Decomposition

A method for reducing controllers for systems described by partial di erential equations (PDEs) is presented. This approach di ers from an often used method of reducing the model and then designing the controller. The controller reduction is accomplished by projection of a large scale nite element approximation of the PDE controller onto low order bases that are computed using the proper orthog...

Snapshot Location in Proper Orthogonal Decomposition for Linear and Semi-linear Parabolic Partial Differential Equations

It is well-known that the performance of POD and POD-DEIM methods depends on the selection of the snapshot locations. In this work, we consider the selections of the locations for POD and POD-DEIM snapshots for spatially semi-discretized linear or semi-linear parabolic PDEs. We present an approach that for a fixed number of snapshots the optimal locations may be selected such that the global di...