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A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering

H. T. Banks
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
We do not plan to review this book.

Introduction to Functional Analysis in Applications
Example 1: Heat Equation
Some Preliminaries: Hilbert, Banach, and Other Spaces Useful in Operator Theory
Return to Example 1: Heat Equation
Example 2: General Transport Equation
Example 3: Delay Systems–Insect/Insecticide Models
Example 4: Probability Measure Dependent Systems — Maxwell’s Equations

Example 5: Structured Population Models

Semigroups and Infinitesimal Generators
Basic Principles of Semigroups
Infinitesimal Generators

Introduction to Generation Theorems
Hille-Yosida Theorems
Results from the Hille-Yosida Proof
Corollaries to Hille-Yosida
Lumer-Phillips and Dissipative Operators
Examples Using Lumer-Phillips Theorem

Adjoint Operators and Dual Spaces
Adjoint Operators
Dual Spaces and Strong, Weak, and Weak* Topologies
Examples of Spaces and Their Duals
Return to Dissipativeness for General Banach Spaces
More on Adjoint Operators
Examples of Computing Adjoints

Gelfand Triple, Sesquilinear Forms, and Lax-Milgram
Example 6: The Cantilever Beam
The Beam Equation in the Form x derivative = Ax + F
Gelfand Triples
Sesquilinear Forms
Lax-Milgram (Bounded Form)
Lax-Milgram (Unbounded Form)
Summary Remarks and Motivation

Analytic Semigroups
Example 1: The Heat Equation (again)
Example 2: The Transport Equation (again)
Example 6: The Beam Equation (again)
Summary of Results on Analytic Semigroup Generation by Sesquilinear Forms
Tanabe Estimates (on "Regular Dissipative Operators")
Infinitesimal Generators in a General Banach Space

Abstract Cauchy Problems

General Second-Order Systems
Introduction to Second-Order Systems
Results for σ2 V-elliptic
Results for σ2 H-semielliptic
Stronger Assumptions for σ2

Weak Formulations for Second-Order Systems
Model Formulation
Discussion of the Model
Theorems 9.1 and 9.2: Proofs

Inverse or Parameter Estimation Problems
Approximation and Convergence
Some Further Remarks

"Weak" or "Variational Form"

Finite Element Approximations and the Trotter-Kato Theorems
Finite Elements
Trotter-Kato Approximation Theorem

Delay Systems: Linear and Nonlinear
Linear Delay Systems and Approximation
Modeling of Viral Delays in HIV Infection Dynamics
Nonlinear Delay Systems
State Approximation and Convergence for Nonlinear Delay Systems
Fixed Delays versus Distributed Delays

Weak* Convergence and the Prohorov Metric in Inverse Problems
Populations with Aggregate Data, Uncertainty, and PBM
A Prohorov Metric Framework for Inverse Problems
Metrics on Probability Spaces
Example 5: The Growth Rate Distribution Model and Inverse Problem in Marine Populations

The Prohorov Metric in Optimization and Optimal Design Problems
Two Player Min-Max Games with Uncertainty
Optimal Design Techniques
Generalized Curves and Relaxed Controls of Variational Theory
Preisach Hysteresis in Smart Materials
NPML and Mixing Distributions in Statistical Estimation

Control Theory for Distributed Parameter Systems
Abstract Formulation
Infinite Dimensional LQR Control: Full State Feedback
The Finite Horizon Control Problem
The Infinite Horizon Control Problem

Families of Approximate Control Problems
The Finite Horizon Problem Approximate Control Gains
The Infinite Horizon Problem Approximate Control Gains