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Control of Random PDEs: An Overview

  • Francisco J. Marín
  • Jesús Martínez-Frutos
  • Francisco PeriagoEmail author
Chapter
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 17)

Abstract

This work reviews theoretical and numerical concepts in the emergent field of optimal control of partial differential equations under uncertainty. The following topics are considered: uncertainty modelling in control problems using probabilistic tools, variational formulation of partial differential equations with random inputs, robust and risk averse formulations of optimal control problems, and numerical resolution methods. The exposition is focused on running the path starting from uncertainty modelling and ending in the practical implementation of numerical schemes for the numerical approximation of the considered problems. To this end, a selected number of illustrative examples is analysed.

Keywords

Uncertainty quantification Partial differential equations with random inputs Stochastic expansion methods Robust optimal control Risk averse control 

Notes

Acknowledgements

Work supported by projects MTM2013-47053 from Ministerio de Economía y Competitividad (Spain), the AEI/FEDER and UE under the contract DPI2016-77538-R, and 19274/PI/14 from Fundación Séneca (Agencia de Ciencia y Tecnología de la Región de Murcia, Spain). The first author was also supported by a Ph.D. grant from Fundación Séneca.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Francisco J. Marín
    • 1
  • Jesús Martínez-Frutos
    • 2
  • Francisco Periago
    • 1
    Email author
  1. 1.Departamento de Matemática Aplicada y EstadísticaUniversidad Politécnica de CartagenaCartagenaSpain
  2. 2.Departamento de Estructuras y ConstrucciónUniversidad Politécnica de CartagenaCartagenaSpain

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