Banks H.T. A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering

New York: Chapman and Hall/CRC, 2012. — 278 p.A Modern Framework Based on Time-Tested Material
A Functional Analysis Framework for Modeling, Essystems. 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.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
Families of Approximate Control Problems