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

ISBN: 9781439880838 出版年：2012 页码：278 Banks, H T CRC Press

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 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 sigma2 V-elliptic Results for sigma2 H-semielliptic Stronger Assumptions for sigma2 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 Motivation 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 References Index