Optimal Control of PDEs under Uncertainty

An introduction with application to optimal shape design of structures

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.