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Optimal Control of Partial Differential Equations: Theory, Methods and Applications

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Synopses & Reviews

Publisher Comments:

"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 andadjoint 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 problemswith 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 nonlinearpartial 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, Trèoltzsch 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."--Publisher's description.

Book News Annotation:

Optimal control theory deals with finding control functions that minimize cost functions for systems described by differential equations. This book focuses on optimal control problems in which the state equation is an elliptic or parabolic partial differential equation. Topics include 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. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Optimal control theory deals with finding control functions that minimize cost functions for systems described by differential equations. This book focuses on optimal control problems in which the state equation is an elliptic or parabolic partial differential equation. Topics include 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. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)

Product Details

ISBN:
9780821849040
Subtitle:
Theory, Methods and Applications
Author:
Troltzsch, Fredi
:
Sprekels, Jurgen (TRN)
Publisher:
Amer Mathematical Society
Subject:
Differential equations, partial
Publication Date:
2010-04-23
Binding:
Hardcover
Grade Level:
SG
Language:
English

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Related Subjects

History and Social Science » Economics » General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Differential Equations

Optimal Control of Partial Differential Equations: Theory, Methods and Applications New Hardcover
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Product details pages American Mathematical Society - English 9780821849040 Reviews:
"Synopsis" by , Optimal control theory deals with finding control functions that minimize cost functions for systems described by differential equations. This book focuses on optimal control problems in which the state equation is an elliptic or parabolic partial differential equation. Topics include 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. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)
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