Optimal Control of PDEs under Uncertainty

An Introduction with Application to Optimal Shape Design of Structures

  • Jesús Martínez-Frutos
  • Francisco Periago Esparza

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Jesús Martínez-Frutos, Francisco Periago Esparza
    Pages 1-8
  3. Jesús Martínez-Frutos, Francisco Periago Esparza
    Pages 9-29
  4. Jesús Martínez-Frutos, Francisco Periago Esparza
    Pages 31-44
  5. Jesús Martínez-Frutos, Francisco Periago Esparza
    Pages 45-78
  6. Jesús Martínez-Frutos, Francisco Periago Esparza
    Pages 79-90
  7. Jesús Martínez-Frutos, Francisco Periago Esparza
    Pages 91-108
  8. Jesús Martínez-Frutos, Francisco Periago Esparza
    Pages 109-120
  9. Back Matter
    Pages 121-123

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.


Partial differential equations with random inputs Stochastic expansion methods Robust optimal control Risk averse optimization Structural shape optimization under uncertainty

Authors and affiliations

  • Jesús Martínez-Frutos
    • 1
  • Francisco Periago Esparza
    • 2
  1. 1.Computational Mechanics and Scientific Computing Group, Department of Structures and ConstructionTechnical University of CartagenaCartagenaSpain
  2. 2.Department of Applied Mathematics and StatisticsTechnical University of CartagenaCartagenaSpain

Bibliographic information

  • DOI
  • Copyright Information The Author(s), under exclusive license to Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-98209-0
  • Online ISBN 978-3-319-98210-6
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site