Optimal Control Problems for Partial Differential Equations on Reticulated Domains

Approximation and Asymptotic Analysis

By: Peter I. Kogut, Günter R. Leugering

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Hardcover | 9 September 2011

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Hardcover
654 Pages

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23.39 x 15.6 x 3.51

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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.

Industry 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 Troeltzsch, Zentralblatt MATH, Vol. 1253, 2013)

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