Modeling and control of physical processes using proper orthogonal decomposition

Modeling and Control of Physical Processes using Proper Orthogonal Decomposition

Proper orthogonal decomposition (POD) technique (or the Karhunan Lo eve procedure) has been used to obtain low dimensional dynamical models of many applications in engineering and science. In principle, the idea is to start with an ensemble of data, called snapshots, collected from an experiment or a numerical procedure of a physical system. The POD technique is then used to produce a set of ba...

Modeling of transitional channel flow using balanced proper orthogonal decomposition

We study reduced-order models of three-dimensional perturbations in linearized channel flow using balanced proper orthogonal decomposition BPOD . The models are obtained from three-dimensional simulations in physical space as opposed to the traditional single-wavenumber approach, and are therefore better able to capture the effects of localized disturbances or localized actuators. In order to a...

Improvement of Reduced Order Modeling based on Proper Orthogonal Decomposition

This report focuses on improving the stability as well as the approximation properties of Reduced Order Models (ROM) based on Proper Orthogonal Decomposition (POD). The ROM is obtained by seeking a solution belonging to the POD subspace and that at the same time minimizes the Navier-Stokes residuals. We propose a modified ROM that directly incorporates the pressure term in the model. The ROM is...

Proper Orthogonal Decomposition: Applications in Optimization and Control

Nonlinear Robust and Optimal Control Via Proper Orthogonal Decomposition

In this paper, a methodology based on proper orthogonal decomposition (POD) for computing approximate closed-loop optimal or robust control laws for finite-dimensional nonlinear systems is proposed. The solution can be obtained on any arbitrary domain of the state space represented by a multidimensional grid. The method only requires the computation of a limited number of well-conditioned two-p...