Title: A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering Author: H.T. Banks ISBN: 1439880832 / 9781439880838 Format: Hard Cover Pages: 280 Publisher: CHAPMAN & HALL Year: 2012 Availability: Out of Stock
Description
Contents
A Modern Framework Based on Time-Tested Material
A 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 Mechanics
Through 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.
Preface
Chapter 1 : Introduction to Functional Analysis in Applications Chapter 2 : Semigroups and Infinitesimal Generators Chapter 3 : Generators Chapter 4 : Adjoint Operators and Dual Spaces Chapter 5 : Gelfand Triple, Sesquilinear Forms, and Lax-Milgram Chapter 6 : Analytic Semigroups Chapter 7 : Abstract Cauchy Problems Chapter 8 : General Second-Order Systems Chapter 9 : Weak Formulations for Second-Order Systems Chapter 10 : Inverse or Parameter Estimation Problems Chapter 11 : "Weak" or "Variational Form" Chapter 12 : Finite Element Approximations and the Trotter-Kato Theorems Chapter 13 : Delay Systems : Linear and Nonlinear Chapter 14 : Weak Convergence and the Prohorov Metric in Inverse Problems Chapter 15 : The Prohorov Metric in Optimization and Optimal Design Problems Chapter 16 : Control Theory for Distributed Parameter Systems Chapter 17 : Families of Approximate Control Problems