J. Martínez-Frutos, Robust Optimal Design of Structures using Stochastic Metamodels, Doctoral dissertation, Technical University of Cartagena.
J. Martínez-Frutos, D. Herrero-Pérez, Massively Parallel Evolutionary Structural Optimization for High Resolution Architectural Design. Advances in Parallel, Distributed, Grid and Cloud Computing for...
 

Optimal Control of PDE under Uncertainty

Optimal Control of PDEs under Uncertainty

An introduction with application to optimal shape design of structures

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About this book:

This book gives a direct and comprehensive introduction to the theoretical and numerical concepts in the emergent field of optimal control of partial differential equations (PDEs) under uncertainty. The main objective of the book is to provide
graduate students and researchers with a smooth transition from optimal control of deterministic PDEs to optimal control of random PDEs. Coverage includes uncertainty modelling in control problems, variational formulation of PDEs with random inputs, robust and risk-averse formulations of optimal control problems, existence theory and numerical resolution methods. The exposition is focused on running the hole 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 are analysed in detail along the book. Computer codes, written in MatLab, for all these examples are provided.

Table of Contents:

  • 1
    Introd​uction.
  • 2
    Mathematical Preli​minaries.
  • 3
    Mathematical Analysis of Optimal Control Problems Under Uncertainty.
  • 4
    Numerical Resolution of Robust Optimal Control Problems.
  • 5
    Numerical Resolution of Risk Averse Optimal Control Problems.
  • 6
    Structural Optimization Under Uncertainty.
  • 7
    Miscellaneous Topics and Open Problems.

Multimedia material (online lectures)

A polynomial chaos-based approach to risk-averse piezoelectric control of random vibrations of beams

Marín, Francisco J; Martínez-Frutos, Jesús; Periago, Francisco

A polynomial chaos-based approach to risk-averse piezoelectric control of random vibrations of beams Journal Article

International Journal for Numerical Methods in Engineering, 115 (6), pp. 738-755, 2018, ISSN: 1097-0207.

Abstract | BibTeX | Links:

Robust Optimal Design of Quantum Electronic Devices

Morales, Ociel; Periago, Francisco; Vallejo, José A

Robust Optimal Design of Quantum Electronic Devices Journal Article Open Access

Mathematical Problems in Engineering, 2018 , pp. 10, 2018, ISSN: 2331-8422.

Abstract | BibTeX | Links:

Risk-averse structural topology optimization under random fields using stochastic expansion methods

Martínez-Frutos, Jesús; Herrero-Pérez, David; Kessler, Mathieu; Periago, Francisco

Risk-averse structural topology optimization under random fields using stochastic expansion methods Journal Article

Computer Methods in Applied Mechanics and Engineering, 330 , pp. 180-206, 2018, ISSN: 0045-7825.

Abstract | BibTeX | Links:

Robust Averaged Control of Vibrations for the Bernoulli-Euler Beam Equation

Marín, Francisco J; Martínez-Frutos, Jesús; Periago, Francisco

Robust Averaged Control of Vibrations for the Bernoulli-Euler Beam Equation Journal Article

Journal of Optimization Theory and Applications, 174 (2), pp. 428–454, 2017, ISSN: 1573-2878.

Abstract | BibTeX | Altmetric | Links:

Robust optimal Robin boundary control for the transient heat equation with random input data

Martínez-Frutos, Jesús; Kessler, Mathieu; Münch, Arnaud; Periago, Francisco

Robust optimal Robin boundary control for the transient heat equation with random input data Journal Article

International Journal for Numerical Methods in Engineering, 108 (2), pp. 116–135, 2016, ISSN: 1097-0207.

Abstract | BibTeX | Altmetric | Links:

Robust shape optimization of continuous structures via the level set method

Martínez-Frutos, Jesús; Herrero-Pérez, David; Kessler, Mathieu; Periago, Francisco

Robust shape optimization of continuous structures via the level set method Journal Article

Computer Methods in Applied Mechanics and Engineering, 305 (Supplement C), pp. 271 - 291, 2016, ISSN: 0045-7825.

Abstract | BibTeX | Altmetric | Links:

Robust optimal shape design for an elliptic PDE with  uncertainty in its input data

Martínez-Frutos, Jesús; Kessler, Mathieu; Periago, Francisco

Robust optimal shape design for an elliptic PDE with uncertainty in its input data Journal Article

ESAIM: COCV, 21 (4), pp. 901-923, 2015.

Abstract | BibTeX | Altmetric | Links: