Optimal Control of PDEs under Uncertainty: An Introduction with Application to Optimal Shape Design of Structures

Optimal Control of PDEs under Uncertainty 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 modeling 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 focuses on the entire path, starting from uncertainty modeling 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 analyzed in detail throughout the book. MATLAB codes for these examples are available for download online. This book is for graduate students and researchers in engineering, physics, and mathematics who are interested in optimal control and optimal design for random partial differential equations.