Optimal control problems for partial differential equations on reticulated domains : approximation and asymptotic analysis
Author(s)
Bibliographic Information
Optimal control problems for partial differential equations on reticulated domains : approximation and asymptotic analysis
（Systems & control）
Birkhäuser, c2011
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Includes bibliographical reference (p. 621-633) and index
Description and Table of Contents
Description
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.
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 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.
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