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Optimal Control Problems for Partial Differential Equations on Reticulated Domains

Approximation and Asymptotic Analysis
BuchGebunden
636 Seiten
Englisch
Springererschienen am09.09.2011
This book offers a method based on asymptotic analysis aimed at combining techniques of homogenization and approximation to cover optimal control problems defined on reticulated domains, networked systems such as lattice, honeycomb, or hierarchical structures.mehr
Verfügbare Formate
BuchGebunden
EUR113,50
E-BookPDF1 - PDF WatermarkE-Book
EUR96,29

Produkt

KlappentextThis book offers a method based on asymptotic analysis aimed at combining techniques of homogenization and approximation to cover optimal control problems defined on reticulated domains, networked systems such as lattice, honeycomb, or hierarchical structures.

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr
Kritik
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)mehr

Schlagworte