Sensitivity analysis approach for reduced-order approximations of optimal control problems governed by Burgers equation

The reduced‐order model of the optimal control problem governed by Burgers equation is derived using the proper orthogonal decomposition (POD) method. The reduced‐order solution depending on parameters, which are different from the nominal values, may not be accurate if the POD basis functions depending on the nominal values are used to derive the reduced‐order model. It is known that Burgers equation is sensitive to the perturbations in the diffusion term, so we use the sensitivity information to improve the robustness of the POD solution by generating two new bases: extrapolated and expanded POD basis. We compare these different bases in terms of accuracy, robustness, and computational time