Overview
- Applications from mechanics and material sciences have been simplified so that prerequisite knowledge in those areas is not required
- Methods described are useful for researchers working with reticulated—or networked—systems, including chemical and civil engineers and materials scientists
- Synthesizes previous results of the authors with those of scientists across the discipline to provide a fresh look at the subject
- Can be used as an advanced textbook on abstract optimal control problems, while the second part of the book serves as a research monograph where stratified applications are discussed
- Includes supplementary material: sn.pub/extras
Part of the book series: Systems & Control: Foundations & Applications (SCFA)
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About this book
Optimal control of partial differential equations (PDEs) is a well-established discipline in mathematics with many interfaces to science and engineering. During the development of this area, the complexity of the systems to be controlled has also increased significantly; however, the numerical realization of these complex systems has become an issue in scientific computing, as the number of variables involved may easily exceed a couple of million.
In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. They aim at combining techniques of homogenization and approximation in order to cover optimal control problems defined on reticulated domains, networked systems such as lattice, honeycomb, or hierarchical structures. Because of these structures' complicated geometry, the asymptotic analysis is even more important, as a direct numerical computation of solutions would be extremely difficult. The work's first part can be used as an advanced textbook on abstract optimal control problems, in particular on reticulated domains, while the second part serves as a research monograph where stratified applications are discussed.
Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains and networked systems.
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Table of contents (16 chapters)
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Front Matter
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Asymptotic Analysis of Optimal Control Problems for Partial Differential Equations: Basic Tools
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Front Matter
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Optimal Control Problems on Periodic Reticulated Domains: Asymptotic Analysis and Approximate Solutions
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Front Matter
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Optimal Control Problems on Periodic Reticulated Domains: Asymptotic Analysis and Approximate Solutions
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Back Matter
Reviews
From the reviews:
“The book under review aims to introduce the reader to various classes of optimal control problems (briefly OCP) governed by partial differential equations and to several applications to problems in engineering that can be modeled by them. … The book is very well conceived and the material is organized in a clear and complete way, starting from basic tools such as measure theory, Sobolev spaces, functional analysis, and general variational problems.” (Giuseppe Buttazzo, Mathematical Reviews, August, 2013)
“This book introduces in the mathematical world of optimal control problems posed in reticulated domains. … a great number of very nice and well written examples illustrate the main difficulties behind the questions and the reasons for posing them. The book provides a very good introduction into this important topic and may serve as the basis for a one semester course on optimal control in reticulated domains and for an associated seminary, where specific aspects of the theory can be discussed.” (Fredi Tröltzsch, Zentralblatt MATH, Vol. 1253, 2013)
Authors and Affiliations
Bibliographic Information
Book Title: Optimal Control Problems for Partial Differential Equations on Reticulated Domains
Book Subtitle: Approximation and Asymptotic Analysis
Authors: Peter I. Kogut, Günter R. Leugering
Series Title: Systems & Control: Foundations & Applications
DOI: https://doi.org/10.1007/978-0-8176-8149-4
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Hardcover ISBN: 978-0-8176-8148-7Published: 09 September 2011
eBook ISBN: 978-0-8176-8149-4Published: 09 September 2011
Series ISSN: 2324-9749
Series E-ISSN: 2324-9757
Edition Number: 1
Number of Pages: XVI, 636
Number of Illustrations: 26 b/w illustrations
Topics: Systems Theory, Control, Control and Systems Theory, Calculus of Variations and Optimal Control; Optimization, Partial Differential Equations, Mathematical and Computational Engineering, Solid Mechanics