Optimal Control of Partial Differential Equations: Analysis, Approximation, and Applications

This book is about optimal control problems (OCPs) for partial differential equations (PDEs), covering the theoretical analysis, numerical methods, and applications to practical problems. It evolved from courses taught by the authors at Politecnico di Milano and is suitable for readers with varying mathematical backgrounds.

Format: Paperback / softback
Length: 498 pages
Publication date: 11 December 2022
Publisher: Springer Nature Switzerland AG

This comprehensive book on optimal control problems (OCPs) for partial differential equations (PDEs) is the result of a series of courses taught by the authors at Politecnico di Milano. It spans from the theoretical setup and rigorous analysis of OCPs to the derivation of system of optimality conditions, the proposition of suitable numerical methods, their formulation, analysis, and application to a wide range of practical problems.

The first introductory chapter provides an overview of representative OCPs and highlights the associated mathematical challenges. The rest of the book is organized into three parts:

Part I introduces preliminary concepts of OCPs for algebraic and dynamical systems.

Part II focuses on OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions.

Part III explores more general classes of OCPs that underpin advanced applications.

The book progresses from simple problems that allow a hands-on treatment to a general framework suitable for tackling a broader class of problems. Numerous pseudocodes are included to facilitate the implementation of the algorithms illustrated throughout the text.

This book is designed for readers with varying mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. Applied mathematicians, computational scientists, and engineers will find it valuable for approaching OCPs in complex applications with a constructive mindset.

Weight: 972g
Dimension: 254 x 178 (mm)
ISBN-13: 9783030772284
Edition number: 1st ed. 2021