Optimal Control Problems for Partial Differential Equations on Reticulated Domains: Approximation and Asymptotic Analysis (Systems & Control: Foundations & Applications)
Language: English
Published by Birkhäuser, 2011
Series: Book 30 of 55 - Systems & Control: Foundations & Applications
- Hardcover
- New
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- Title
- Optimal Control Problems for Partial Differential Equations on Reticulated Domains: Approximation and Asymptotic Analysis (Systems & Control: Foundations & Applications)
- Author
- Kogut, Peter I.; Leugering, Günter R.
- Publisher
- Birkhäuser
- Publication year
- 2011
- Condition
- New
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 0817681485
- ISBN 13
- 9780817681487
- Item weight
- 1,206 grams
- Series
- Book 30 of 55: Systems & Control: Foundations & Applications
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 explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation.
Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains.
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From the Back Cover
After over 50 years of increasing scientific interest, optimal control of partial differential equations (PDEs) has developed into a well-established discipline in mathematics with myriad applications to science and engineering. As the field has grown, so too has the complexity of the systems it describes; the numerical realization of optimal controls has become increasingly difficult, demanding ever more sophisticated mathematical tools.
A comprehensive monograph on the subject, Optimal Control of Partial Differential Equations on Reticulated Domains is intended to address some of the obstacles that face researchers today, particularly with regard to multi-scale engineering applications involving hierarchies of grid-like domains. Bringing original results together with others previously scattered across the literature, it tackles computational challenges by exploiting asymptotic analysis and harnessing differences between optimal control problems and their underlying PDEs.
The book consists of two parts, the first of which can be viewed as a compendium of modern optimal control theory in Banach spaces. The second part is a focused, in-depth, and self-contained study of the asymptotics of optimal control problems related to reticulated domains―the first such study in the literature. Specific topics covered in the work include:
* a mostly self-contained mathematical theory of PDEs on reticulated domains;
* the concept of optimal control problems for PDEs in varying such domains, and hence, in varying Banach spaces;
* convergence of optimal control problems in variable spaces;
* an introduction to the asymptotic analysis of optimal control problems;
* optimal control problems dealing with ill-posed objects on thin periodic structures, thick periodic singular graphs, thick multi-structures with Dirichlet and Neumann boundary controls, and coefficients on reticulated structures.
Serving as both a text on abstract optimal control problems and a monograph where specific applications are explored, this book is an excellent reference for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains.
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