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Kogut, Peter I.; Leugering, Günter R.

Optimal Control Problems for Partial Differential Equations on Reticulated Domains Approximation and Asymptotic Analysis (Gebundene Ausgabe)

Reihe: Systems & Control: Foundations & Applications

Springer Basel AG, Birkhäuser Boston, Oktober 2011

Edition - 636 S. - Sprache: Englisch - 26 schwarz-weiße Abbildungen - 241x159x43 mm Book

ISBN: 0817681485 EAN: 9780817681487

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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Applications from mechanics and material sciences have been simplified so that prerequisite knowledge in those areas is not requiredMethods described are useful for researchers working with reticulated-or networked-systems, including chemical and civil engineers and materials scientistsSynthesizes 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


Introduction.- Part I. Asymptotic Analysis of Optimal Control Problems for Partial Differential Equations: Basic Tools.- Background Material on Asymptotic Analysis of External Problems.- Variational Methods of Optimal Control Theory.- Suboptimal and Approximate Solutions to External Problems.- Introduction to the Asymptotic Analysis of Optimal Control Problems: A Parade of Examples.- Convergence Concepts in Variable Banach Spaces.- Convergence of Sets in Variable Spaces.- Passing to the Limit in Constrained Minimization Problems.- Part II. Optimal Control Problems on Periodic Reticulated Domains: Asymptotic Analysis and Approximate Solutions.- Suboptimal Control of Linear Steady-States Processes on Thin Periodic Structures with Mixed Boundary Controls.- Approximate Solutions of Optimal Control Problems for Ill-Posed Objects on Thin Periodic Structures.- Asymptotic Analysis of Optimal Control Problems on Periodic Singular Structures.- Suboptimal Boundary Control of Elliptic Equations in Domains with Small Holes.- Asymptotic Analysis of Elliptic Optimal Control Problems in Thick Multi-Structures with Dirichlet and Neumann Boundary Controls.- Gap Phenomenon in Modeling of Suboptimal Controls to Parabolic Optimal Control Problems in Thick Multi-Structures.- Boundary Velocity Suboptimal Control of Incompressible Flow in Cylindrically Perforated Domains.- Optimal Control Problems in Coefficients: Sensitivity Analysis and Approximation.- References.- Index.


From the reviews: "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)

ISBN 0-817681-48-5, ISBN 0-81-768148-5, ISBN 0-81768-148-5, ISBN 0-817-68148-5, ISBN 0-8176-8148-5

ISBN 978-0-817681-48-7, ISBN 978-0-81-768148-7, ISBN 978-0-81768-148-7, ISBN 978-0-817-68148-7, ISBN 978-0-8176-8148-7

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