A functional analysis framework for modeling, estimation, and control in science and engineering
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Bibliographic Information
A functional analysis framework for modeling, estimation, and control in science and engineering
CRC Press, c2012
- : hbk
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Includes bibliographical references and index
Description and Table of Contents
Description
A Modern Framework Based on Time-Tested MaterialA Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems. Drawing on his extensive research and teaching from the past 20 years, the author explains how functional analysis can be the basis of modern partial differential equation (PDE) and delay differential equation (DDE) techniques.
Recent Examples of Functional Analysis in Biology, Electromagnetics, Materials, and MechanicsThrough numerous application examples, the book illustrates the role that functional analysis-a classical subject-continues to play in the rigorous formulation of modern applied areas. The text covers common examples, such as thermal diffusion, transport in tissue, and beam vibration, as well as less traditional ones, including HIV models, uncertainty in noncooperative games, structured population models, electromagnetics in materials, delay systems, and PDEs in control and inverse problems. For some applications, computational aspects are discussed since many problems necessitate a numerical approach.
Table of Contents
Introduction to Functional Analysis in Applications. Semigroups and Infinitesimal Generators. Generators. Adjoint Operators and Dual Spaces. Gelfand Triple, Sesquilinear Forms, and Lax-Milgram. Analytic Semigroups. Abstract Cauchy Problems. General Second-Order Systems. Weak Formulations for Second-Order Systems. Inverse or Parameter Estimation Problems. "Weak" or "Variational Form". Finite Element Approximations and the Trotter-Kato Theorems. Delay Systems: Linear and Nonlinear. Weak* Convergence and the Prohorov Metric in Inverse Problems. The Prohorov Metric in Optimization and Optimal Design Problems. Control Theory for Distributed Parameter Systems. Families of Approximate Control Problems. References. Index.
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