Optimal Control of PDEs under Uncertainty

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.

• 1 Introduction.- 2 Mathematical Preliminaires.- 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.

“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)