Optimal Control Partial Differential by Fredi Troltzsch (40 results)
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Published by American Mathematical Society, 2024
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Published by American Mathematical Society, US, 2010
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Paperback. Condition: New. 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 opt…imal 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.
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Published by American Mathematical Society, 2024
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Published by American Mathematical Society, 2024
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Taschenbuch. Condition: Neu. Optimal Control of Partial Differential Equations | International Conference in Chemnitz, Germany, April 20-25, 1998 | Karl-Heinz Hoffmann (u. a.) | Taschenbuch | International Series of Numerical Mathematics | viii | Englisch | 2012 | Birkhäuser | EAN 9783034897310 | Verantwortliche Person für die E…U: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and is of interest to… mathematicians and scientists working in the field.
Language: English
Published by American Mathematical Society, 2024
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Published by American Mathematical Society, 2010
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Optimal Control of Partial Differential Equations: International Conference in Chemnitz, Germany, April 20-25, 1998
Hoffmann, Karl-Heinz (Editor)/ Leugering, Gunter (Editor)/ Troltzsch, Fredi (Editor)
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and is of interest to mathem…aticians and scientists working in the field.
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Condition: New. The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and is of interest to mathemat.
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Published by American Mathematical Society, US, 2010
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Paperback. Condition: New. 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 opt…imal 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.
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Condition: Sehr gut. Zustand: Sehr gut | Seiten: 356 | Sprache: Englisch | Produktart: Bücher | The articles contained in this volume are related to presentations at the inter- tional ¿Conference on Optimal Control of Coupled Systems of Partial Di?erential Equations¿, held at the ¿Mathematisches Forschungsinstitut Oberwolfach¿ f…rom March, 2 to 8, 2008. The contributions by internationally well-known scientists in the ?eld of Applied Mathematics cover various topics as controllability, feedba- control,optimalitysystems,model-reductiontechniques,analysisandoptimalc- trol of ?ow problems and ?uid-structure interactions, as well as problems of shape and topology optimization. The applications considered range from the optimi- tion and control of quantum mechanical systems, the optimal design of airfoils, optimal control of crystal growth, the optimization of shape and topology in en- neering to switching or hybrid systems. The applications are thus across all time and length scales, and range from smooth to non-smooth models. The ?eld of optimization and control of systems governed by partial d- ferential equations and variational inequalities is a very active area of research in Applied Mathematics and in particular in numerical analysis, scienti?c c- puting and optimization with a growing impact on engineering applications. In return, the ?eld bene?ts from fascinating and challenging applications in that new mathematical often multiscale-modeling and new numerical tools as well as novel optimization results and corresponding iterative strategies arerequired in order to handle these problems. In particular,it becomes amply clear that constraints have to be taken into account, both on the control- and design-variables as well as on the state variablesandthe domains oftheir governingmodels.
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - The articles contained in this volume are related to presentations at the inter- tional Conference on Optimal Control of Coupled Systems of Partial Di erential Equations , held at the Mathematisches Forschungsinstitut Oberwolfach from March, 2 to 8, 2008.… The contributions by internationally well-known scientists in the eld of Applied Mathematics cover various topics as controllability, feedba- control,optimalitysystems,model-reductiontechniques,analysisandoptimalc- trol of ow problems and uid-structure interactions, as well as problems of shape and topology optimization. The applications considered range from the optimi- tion and control of quantum mechanical systems, the optimal design of airfoils, optimal control of crystal growth, the optimization of shape and topology in en- neering to switching or hybrid systems. The applications are thus across all time and length scales, and range from smooth to non-smooth models. The eld of optimization and control of systems governed by partial d- ferential equations and variational inequalities is a very active area of research in Applied Mathematics and in particular in numerical analysis, scienti c c- puting and optimization with a growing impact on engineering applications. In return, the eld bene ts from fascinating and challenging applications in that new mathematical often multiscale-modeling and new numerical tools as well as novel optimization results and corresponding iterative strategies arerequired in order to handle these problems. In particular,it becomes amply clear that constraints have to be taken into account, both on the control- and design-variables as well as on the state variablesandthe domains oftheir governingmodels.
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and i…s of interest to mathematicians and scientists working in the field. 340 pp. Englisch.
