Reduced Order Optimal Control Using Proper Orthogonal Decomposition Sensitivities
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In general, reduced-order model (ROM) solutions obtained using proper orthogonal decomposition (POD) at a single parameter cannot approximate the solutions at other parameter values accurately. In this paper, parameter sensitivity analysis is performed for POD reduced order optimal control problems (OCPs) governed by linear diffusion-convection-reaction equations. The OCP is discretized in space and time by discontinuous Galerkin (dG) finite elements. We apply two techniques, extrapolating and expanding the POD basis, to assess the accuracy of the reduced solutions for a range of parameters. Numerical results are presented to demonstrate the performance of these techniques to analyze the sensitivity of the OCP with respect to the ratio of the convection to the diffusion terms.
KeywordsOptimal Control Problem Proper Orthogonal Decomposition Proper Orthogonal Decomposition Mode Parameter Sensitivity Analysis Proper Orthogonal Decomposition Basis
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