Titlebook: Optimal Control of PDEs under Uncertainty; An Introduction with Jesús Martínez-Frutos,Francisco Periago Esparza Book 2018 The Author(s), un

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Numerical Resolution of Risk Averse Optimal Control Problems,em ., as defined in Sect. 2.2. The numerical approximation of the associated statistics combines an adaptive, anisotropic, non-intrusive, Stochastic Galerkin approach for the numerical resolution of the underlying state and adjoint equations with a standard Monte-Carlo (MC) sampling method for numerical integration in the random domain.

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Jesús Martínez-Frutos,Francisco Periago EsparzaOffers a smooth transition from optimal control of deterministic PDEs to optimal control of random PDEs.Covers uncertainty modelling in control problems, variational formulation of random PDEs, existe

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Miscellaneous Topics and Open Problems,In this final chapter we discuss some related topics to the basic methodology presented in detail in the previous chapters. These topics are related to (i) time-dependent problems, and (ii) physical interpretation of robust and risk-averse optimal controls. We also list a number of challenging problems in the field of control under uncertainty.

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SpringerBriefs in Mathematicshttp://image.papertrans.cn/o/image/702834.jpg

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https://doi.org/10.1007/978-3-319-98210-6Partial differential equations with random inputs; Stochastic expansion methods; Robust optimal contro

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Mathematical Analysis of Optimal Control Problems Under Uncertainty, tensor product of Hilbert spaces or abstract functions, i.e., functions with values in Banach or Hilbert spaces. However, tensor products of Hilbert spaces have the advantage that the numerical approximation of such random PDEs becomes very natural in such a formalism.

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pessimism

Introduction,em’s parameters, such as its geometry, initial and/or boundary conditions, external forces and material properties (diffusion coefficients, elasticity modulus, etc.), induces additional errors, called ..