Overview
- 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
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
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 isadressed to graduate students and researches in Engineering, Physics and Mathematics who are interested in optimal control and optimal design for random partial differential equations.
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Authors and Affiliations
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.
Bibliographic Information
Book Title: Optimal Control of PDEs under Uncertainty
Book Subtitle: An Introduction with Application to Optimal Shape Design of Structures
Authors: Jesús Martínez-Frutos, Francisco Periago Esparza
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-98210-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-98209-0Published: 13 September 2018
eBook ISBN: 978-3-319-98210-6Published: 30 August 2018
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XIX, 123
Number of Illustrations: 8 b/w illustrations, 37 illustrations in colour
Topics: Partial Differential Equations, Mathematical and Computational Engineering, Vibration, Dynamical Systems, Control, Solid Mechanics, Calculus of Variations and Optimal Control; Optimization, Probability Theory and Stochastic Processes