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Optimal Control Problems for Partial Differential Equations on Reticulated Domains: Approximation and Asymptotic Analysis (Systems & Control: Foundations & Applications)

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Optimal Control Problems for Partial Differential Equations on Reticulated Domains: Approximation and Asymptotic Analysis (Systems & Control: Foundations & Applications) Cover

 

Synopses & Reviews

Publisher Comments:

Optimal control of partial differential equations (PDEs) is by now, after more than 50 years of ever increasing scientific interest, 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, so that today fluid-structure interactions, magneto-hydromechanical, or electromagnetical as well as chemical and civil engineering problems can be dealt with. However, the numerical realization of optimal controls based on optimality conditions, together with the simulation of the states, 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 ever-increasingly complex 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 including lattice, honeycomb, and hierarchical structures. The investigation of optimal control problems for such structures is important to researchers working with cellular and hierarchical materials (lightweight materials) such as metallic and ceramic foams as well as bio-morphic material. Other modern engineering applications are chemical and civil engineering technologies, which often involve networked systems. Because of the complicated geometry of these structures--periodic media with holes or inclusions and a very small amount of material along layers or along bars--the asymptotic analysis is even more important, as a direct numerical computation of solutions would be extremely difficult. Specific topics 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,  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.

Synopsis:

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.

Synopsis:

In the development of optimal control, the complexity of the systems

Table of Contents

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

Product Details

ISBN:
9780817681487
Author:
Kogut, Peter I.
Publisher:
Birkhauser
Author:
uuml
Author:
nter
Author:
nter Leugering
Author:
Leugering, G.
Author:
Leugering, Günter R.
Author:
G .
Author:
&
Subject:
Applied
Subject:
Banach spaces
Subject:
Dirichlet optimal control problem
Subject:
lagrange multiplier
Subject:
Neumann boundary control
Subject:
Asymptotic analysis
Subject:
boundary control
Subject:
convergence concepts
Subject:
Elliptic equations
Subject:
gap phenomenon
Subject:
networked systems
Subject:
optimal control problems
Subject:
periodic structures
Subject:
reticulated domains
Subject:
sensitivity analysis
Subject:
variable spaces
Subject:
Systems Theory, Control
Subject:
Control
Subject:
Calculus of Variations and Optimal Control; Optimization
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
Structural Mechanics
Subject:
Mathematics-Applied
Subject:
System Theory
Copyright:
Edition Description:
2011
Series:
Systems & Control: Foundations & Applications
Publication Date:
20110429
Binding:
HARDCOVER
Language:
English
Pages:
652
Dimensions:
235 x 155 mm

Related Subjects

Health and Self-Help » Health and Medicine » Medical Specialties
Science and Mathematics » Materials Science » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Computer
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Systems Theory

Optimal Control Problems for Partial Differential Equations on Reticulated Domains: Approximation and Asymptotic Analysis (Systems & Control: Foundations & Applications) New Hardcover
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Product details 652 pages Springer - English 9780817681487 Reviews:
"Synopsis" by , 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.
"Synopsis" by , In the development of optimal control, the complexity of the systems
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