Model order reduction techniques with a posteriori error control for nonlinear robust optimization governed by partial differential equations. (English) Zbl 1428.35644
Summary: We consider a nonlinear optimization problem governed by partial differential equations with uncertain parameters. It is addressed by a robust worst case formulation. The resulting optimization problem is of bilevel structure and is difficult to treat numerically. We propose an approximate robust formulation that employs linear and quadratic approximations. To speed up the computation, reduced order models based on proper orthogonal decomposition in combination with a posteriori error estimators are developed. The proposed strategy is then applied to the optimal placement of a permanent magnet in the rotor of a synchronous machine with moving rotor. Numerical results are presented to validate the presented approach.
MSC:
| 35Q93 | PDEs in connection with control and optimization |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 90C31 | Sensitivity, stability, parametric optimization |
| 93C20 | Control/observation systems governed by partial differential equations |
Keywords:
model order reduction; PDE constrained optimization; robust optimization; proper orthogonal decomposition; parametrized optimal control problemReferences:
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