A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering  book cover
1st Edition

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

ISBN 9781439880838
Published June 18, 2012 by Chapman & Hall
280 Pages 9 B/W Illustrations

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Book Description

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.

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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H.T. Banks is a Distinguished University Professor and Drexel Professor of Mathematics at North Carolina State University, where he is also the director of the Center for Research in Scientific Computation and co-director of the Center for Quantitative Sciences in Biomedicine. He currently serves on the editorial boards of 14 journals and has published over 425 papers in applied mathematics and engineering journals. A fellow of the IEEE, IoP, SIAM, and AAAS, Dr. Banks has received numerous honors, including the W.T. and Idalia Reid Prize in Applied Mathematics from SIAM, the Lord Robert May Prize from the Journal of Biological Dynamics, and Best Paper Awards from the ASME and ACS.


"The book under review has the valuable advantage of being of interest to both mathematicians and engineers. … appropriate tools are carefully introduced and discussed in detail, and they are readily applied to practical situations related to the models derived from the generic examples. The main thrust of the book consists of those parts and topics of functional analysis that are fundamental to rigorous discussions of practical differential equations and delay systems as they arise in diverse applications and in particular in control and estimation."
—Larbi Berrahmoune, Mathematical Reviews, May 2013