Optimal Control of Partial Differential Equations

Optimal Control of Partial Differential Equations
Author : Fredi Tröltzsch
Publisher : American Mathematical Soc.
Total Pages : 399
Release : 2010
ISBN 10 : 9780821849040
ISBN 13 : 0821849042
Language : EN, FR, DE, ES & NL

Optimal Control of Partial Differential Equations Book 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, Tr'oltzsch 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.


RELATED BOOKS:
Optimal Control of Partial Differential Equations
Language: en
Pages: 399
Authors: Fredi Tröltzsch
Categories: Mathematics
Type: BOOK - Published: 2010 - Publisher: American Mathematical Soc.

"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
Control of Coupled Partial Differential Equations
Language: en
Pages: 384
Authors: Karl Kunisch, Günter Leugering, Jürgen Sprekels, Fredi Tröltzsch
Categories: Mathematics
Type: BOOK - Published: 2007-08-08 - Publisher: Springer Science & Business Media

This volume contains selected contributions originating from the ‘Conference on Optimal Control of Coupled Systems of Partial Differential Equations’, held at the ‘Mathematisches Forschungsinstitut Oberwolfach’ in April 2005. With their articles, leading scientists cover a broad range of topics such as controllability, feedback-control, optimality systems, model-reduction techniques, analysis and optimal
Optimal Control of Systems Governed by Partial Differential Equations
Language: en
Pages: 396
Authors: Jacques-Louis Lions
Categories: Mathematics
Type: BOOK - Published: 1971 - Publisher: Springer Verlag

Books about Optimal Control of Systems Governed by Partial Differential Equations
Controllability of Partial Differential Equations Governed by Multiplicative Controls
Language: en
Pages: 284
Authors: Alexander Y. Khapalov
Categories: Mathematics
Type: BOOK - Published: 2010-05-19 - Publisher: Springer

This monograph addresses the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The methodology is illustrated with a variety of model equations.
Optimal Control Problems for Partial Differential Equations on Reticulated Domains
Language: en
Pages: 636
Authors: Peter I. Kogut, Günter R. Leugering
Categories: Science
Type: BOOK - Published: 2011-09-09 - Publisher: Springer Science & Business Media

In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract