Local improvements to reduced-order approximations of optimal control problems governed by diffusion-convection-reaction equation

Akman, Tuğba
We consider the optimal control problem governed by diffusion-convection-reaction equation without control constraints. The proper orthogonal decomposition (POD) method is used to reduce the dimension of the problem. The POD method may lack accuracy if the POD basis depending on a set of parameters is used to approximate the problem depending on a different set of parameters. To increase the accuracy and the robustness of the basis, we compute five bases additional to the baseline POD in case of the perturbation of the diffusion term, a parameter in the convection field, the reaction term and Tikhonov regularization term. For the first two bases, we use the sensitivity information to extrapolate and expand the baseline POD basis. The other one is based on the subspace angle interpolation method. Multiple snapshot sets are used to derive the last two bases. A-posteriori error estimator is used to analyse the difference between the suboptimal control, computed using the POD basis, and the optimal control. We compare these different bases in terms of accuracy and complexity, investigate the advantages and main drawbacks of them.


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We apply two different strategies for solving unsteady distributed optimal control problems governed by diffusion-convection-reaction equations. In the first approach, the optimality system is transformed into a biharmonic equation in the space time domain. The system is then discretized in space and time simultaneously and solved by an equation-based finite element package, i.e., COMSOL Multiphysics. The second approach is a classical gradient-based optimization method to solve the state and adjoint equati...
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Citation Formats
T. Akman, “Local improvements to reduced-order approximations of optimal control problems governed by diffusion-convection-reaction equation,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, pp. 104–131, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62294.