Optimal Control of Partial Differential Equations (Graduate Studies in Mathematics) by Fredi Troltzsch (PDF)

Description

Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Troltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.

User’s Reviews

Editorial Reviews: Review “The book provides a thorough and self-contained introduction…[It includes] carefully chosen examples…The presentation of the material is clear and self-contained. A great deal of attention is paid to careful exposition of relevant supporting tools from nonlinear analysis and PDEs. …A wealth of examples… [T]his is a very carefully written text with an eye on graduate students wishing to enter the field of PDE optimal control. The material presented is fairly complete, self-contained and well exposed.” —- Irena Lasiecka, Mathematical Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a Mathematics text, not an Optimization or Control Theory text. The author presents his work in an order which often leads to confusion before he reaches a “result” which is a commonplace fact in Optimization. The text also lacks detail in important areas, and not all proofs are included, leaving the reader to search out his many references — I will need to buy 5 other books to get the grounding I had hoped for from this one. I don’t know if there is a better text available on this subject, but I have not been satisfied by this one.

⭐

Keywords

Free Download Optimal Control of Partial Differential Equations (Graduate Studies in Mathematics) in PDF format
Optimal Control of Partial Differential Equations (Graduate Studies in Mathematics) PDF Free Download
Download Optimal Control of Partial Differential Equations (Graduate Studies in Mathematics) 2010 PDF Free
Optimal Control of Partial Differential Equations (Graduate Studies in Mathematics) 2010 PDF Free Download
Download Optimal Control of Partial Differential Equations (Graduate Studies in Mathematics) PDF
Free Download Ebook Optimal Control of Partial Differential Equations (Graduate Studies in Mathematics)