A POD framework to determine robust controls in PDE optimization

Abstract

A strategy for the fast computation of robust controls of PDE models with random-field coefficients is presented. A robust control is defined as the control function that minimizes the expectation value of the objective over all coefficient configurations. A straightforward application of the adjoint method on this problem results in a very large optimality system. In contrast, a fast method is presented where the expectation value of the objective is minimized with respect to a reduced POD basis of the space of controls. Comparison of the POD scheme with the full optimization procedure in the case of elliptic control problems with random reaction terms and with random diffusivity demonstrates the superior computational performance of the POD method.