Download book Optimal Control of Partial Differential Equations : Theory, Methods and Applications
Download book Optimal Control of Partial Differential Equations : Theory, Methods and Applications
Optimal Control of Partial Differential Equations : Theory, Methods and Applications.cFredi Tröltzsch
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Author: Fredi Tröltzsch
Page Count: 112 pages
Published Date: 15 May 2010
Publisher: American Mathematical Society
Publication Country: Providence, United States
Language: English
ISBN: 9780821849040
Download Link: Optimal Control of Partial Differential Equations Theory, Methods and Applications
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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 equation, quadratic cost function 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.
Read online Optimal Control of Partial Differential Equations : Theory, Methods and Applications Buy and read online Optimal Control of Partial Differential Equations : Theory, Methods and Applications Download Optimal Control of Partial Differential Equations : Theory, Methods and Applications ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent Download to iPad/iPhone/iOS, B&N nook Optimal Control of Partial Differential Equations : Theory, Methods and Applications
Optimal Control of Partial Differential Equations : Theory, Methods and Applications.cFredi Tröltzsch
Author: Fredi Tröltzsch
Page Count: 112 pages
Published Date: 15 May 2010
Publisher: American Mathematical Society
Publication Country: Providence, United States
Language: English
ISBN: 9780821849040
Download Link: Optimal Control of Partial Differential Equations Theory, Methods and Applications
---------------------------------------------------------------
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 equation, quadratic cost function 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.
Read online Optimal Control of Partial Differential Equations : Theory, Methods and Applications Buy and read online Optimal Control of Partial Differential Equations : Theory, Methods and Applications Download Optimal Control of Partial Differential Equations : Theory, Methods and Applications ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent Download to iPad/iPhone/iOS, B&N nook Optimal Control of Partial Differential Equations : Theory, Methods and Applications