20171215
We study sparse solutions of optimal control problems governed by elliptic PDEs with uncertain coefficients. Sparsity of controls is achieved by incorporating the \(L^1\)norm of the mean of the pointwise squared controls in the objective. Two optimal control formulations are proposed, one where the solution is a deterministic control that optimizes the mean objective, and a formulation aiming at stochastic controls that all share the same sparsity structure. For the solution of the stochastic control problem, we propose a norm reweighting algorithm, which iterates over functions defined over the physical space only and thus avoids approximation of the random space. Combined with lowrank operator approximations, this results in an efficient solution method that avoids approximation of the uncertain parameter random space. The qualitative structure of the optimal controls and the performance of the solution algorithm are studied numerically using control problems governed by the Laplace and Helmholtz equations. This is joint work with Chen Li (NYU).
Category: CE SeminarTechnische Universität Darmstadt
Graduate School CE
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D64293 Darmstadt

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