SpringerBriefs in Mathematics
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Optimal Control of PDEs under Uncertainty

An Introduction with Application to Optimal Shape Design of Structures

Authors: Martínez-Frutos, Jesús, Periago Esparza, Francisco

  • Offers 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, existence theory and numerical resolution methods
  • Provides computer codes, written in MatLab
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eBook 46,00 €
price for Spain (gross)
  • ISBN 978-3-319-98210-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-3-319-98209-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

This book provides a direct and comprehensive introduction to theoretical and numerical concepts in the emerging field of optimal control of partial differential equations (PDEs) under uncertainty. The main objective of the book is to offer graduate students and researchers 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 focusses on the entire 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 throughout the book. Computer codes, written in MatLab, are provided for all these examples. This book is adressed to graduate students and researches in Engineering, Physics and Mathematics  who are interested in optimal control and optimal design  for random partial differential  equations.


About the authors

Jesús Martínez-Frutos obtained his PhD from the Technical University of Cartagena, Spain, in 2014 and is currently Assistant Professor in the Department of Structures and Construction and a member of the Computational Mechanics and Scientific Computing group at the Technical University of Cartagena, Spain. His research interests are in the field of robust optimal control, structural optimization under uncertainty, efficient methods for high-dimensional uncertainty propagation and high-performance computing using GPUs, with special focus on industrial applications.

Francisco Periago Esparza completed his PhD at the University of Valencia, Spain, in 1999. He is currently Associate Professor in the Department of Applied Mathematics and Statistics and a member of the Computational Mechanics and Scientific Computing group at the Technical University of Cartagena, Spain. His main research interests include optimal control, optimal design and controllability, both at the theoretical level and for applications to engineering problems. During recent years his research has focused on optimal control for random PDEs. 

Reviews

“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.” (Mathematical Reviews, November, 2019)

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Introduction

    Pages 1-8

    Martínez-Frutos, Jesús (et al.)

  • Mathematical Preliminaires

    Pages 9-29

    Martínez-Frutos, Jesús (et al.)

  • Mathematical Analysis of Optimal Control Problems Under Uncertainty

    Pages 31-44

    Martínez-Frutos, Jesús (et al.)

  • Numerical Resolution of Robust Optimal Control Problems

    Pages 45-78

    Martínez-Frutos, Jesús (et al.)

  • Numerical Resolution of Risk Averse Optimal Control Problems

    Pages 79-90

    Martínez-Frutos, Jesús (et al.)

Buy this book

eBook 46,00 €
price for Spain (gross)
  • ISBN 978-3-319-98210-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-3-319-98209-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Optimal Control of PDEs under Uncertainty
Book Subtitle
An Introduction with Application to Optimal Shape Design of Structures
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-319-98210-6
DOI
10.1007/978-3-319-98210-6
Softcover ISBN
978-3-319-98209-0
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XIX, 123
Number of Illustrations
8 b/w illustrations, 37 illustrations in colour
Topics