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

A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering
Author: H.T. Banks
Publisher: CRC Press
Total Pages: 282
Release: 2012-06-18
Genre: Mathematics
ISBN: 1439880832

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.

Optimal Input Signals for Parameter Estimation

Optimal Input Signals for Parameter Estimation
Author: Ewaryst Rafajłowicz
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 202
Release: 2022-03-07
Genre: History
ISBN: 3110351048

The aim of this book is to provide methods and algorithms for the optimization of input signals so as to estimate parameters in systems described by PDE’s as accurate as possible under given constraints. The optimality conditions have their background in the optimal experiment design theory for regression functions and in simple but useful results on the dependence of eigenvalues of partial differential operators on their parameters. Examples are provided that reveal sometimes intriguing geometry of spatiotemporal input signals and responses to them. An introduction to optimal experimental design for parameter estimation of regression functions is provided. The emphasis is on functions having a tensor product (Kronecker) structure that is compatible with eigenfunctions of many partial differential operators. New optimality conditions in the time domain and computational algorithms are derived for D-optimal input signals when parameters of ordinary differential equations are estimated. They are used as building blocks for constructing D-optimal spatio-temporal inputs for systems described by linear partial differential equations of the parabolic and hyperbolic types with constant parameters. Optimality conditions for spatially distributed signals are also obtained for equations of elliptic type in those cases where their eigenfunctions do not depend on unknown constant parameters. These conditions and the resulting algorithms are interesting in their own right and, moreover, they are second building blocks for optimality of spatio-temporal signals. A discussion of the generalizability and possible applications of the results obtained is presented.

Control and Optimization with PDE Constraints

Control and Optimization with PDE Constraints
Author: Kristian Bredies
Publisher: Springer Science & Business Media
Total Pages: 221
Release: 2013-06-12
Genre: Mathematics
ISBN: 3034806310

Many mathematical models of physical, biological and social systems involve partial differential equations (PDEs). The desire to understand and influence these systems naturally leads to considering problems of control and optimization. This book presents important topics in the areas of control of PDEs and of PDE-constrained optimization, covering the full spectrum from analysis to numerical realization and applications. Leading scientists address current topics such as non-smooth optimization, Hamilton–Jacobi–Bellmann equations, issues in optimization and control of stochastic partial differential equations, reduced-order models and domain decomposition, discretization error estimates for optimal control problems, and control of quantum-dynamical systems. These contributions originate from the “International Workshop on Control and Optimization of PDEs” in Mariatrost in October 2011. This book is an excellent resource for students and researchers in control or optimization of differential equations. Readers interested in theory or in numerical algorithms will find this book equally useful.

Controller Design for Distributed Parameter Systems

Controller Design for Distributed Parameter Systems
Author: Kirsten A. Morris
Publisher: Springer Nature
Total Pages: 295
Release: 2020-06-01
Genre: Technology & Engineering
ISBN: 3030349497

This book addresses controller and estimator design for systems that vary both spatially and in time: systems like fluid flow, acoustic noise and flexible structures. It includes coverage of the selection and placement of actuators and sensors for such distributed-parameter systems. The models for distributed parameter systems are coupled ordinary/partial differential equations. Approximations to the governing equations, often of very high order, are required and this complicates both controller design and optimization of the hardware locations. Control system and estimator performance depends not only on the controller/estimator design but also on the location of the hardware. In helping the reader choose the best location for actuators and sensors, the analysis provided in this book is crucial because neither intuition nor trial-and-error is foolproof, especially where multiple sensors and actuators are required, and moving hardware can be difficult and costly. The mechatronic approach advocated, in which controller design is integrated with actuator location, can lead to better performance without increased cost. Similarly, better estimation can be obtained with carefully placed sensors. The text shows how proper hardware placement varies depending on whether, disturbances are present, whether the response should be reduced to an initial condition or whether controllability and/or observability have to be optimized. This book is aimed at non-specialists interested in learning controller design for distributed-parameter systems and the material presented has been used for student teaching. The relevant basic systems theory is presented and followed by a description of controller synthesis using lumped approximations. Numerical algorithms useful for efficient implementation in real engineering systems and practical computational challenges are also described and discussed.

Uncertainty Quantification

Uncertainty Quantification
Author: Ralph C. Smith
Publisher: SIAM
Total Pages: 400
Release: 2013-12-02
Genre: Computers
ISBN: 1611973228

The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.

A Practical Guide to Geometric Regulation for Distributed Parameter Systems

A Practical Guide to Geometric Regulation for Distributed Parameter Systems
Author: Eugenio Aulisa
Publisher: CRC Press
Total Pages: 292
Release: 2015-06-18
Genre: Mathematics
ISBN: 1482240149

A Practical Guide to Geometric Regulation for Distributed Parameter Systems provides an introduction to geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite-dimensional systems. The book also introduces several new control algorithms inspired by geometric invariance and asymptotic attraction for a wid

Fluid-Structure Interaction and Biomedical Applications

Fluid-Structure Interaction and Biomedical Applications
Author: Tomáš Bodnár
Publisher: Springer
Total Pages: 580
Release: 2014-10-13
Genre: Mathematics
ISBN: 3034808224

This book presents, in a methodical way, updated and comprehensive descriptions and analyses of some of the most relevant problems in the context of fluid-structure interaction (FSI). Generally speaking, FSI is among the most popular and intriguing problems in applied sciences and includes industrial as well as biological applications. Various fundamental aspects of FSI are addressed from different perspectives, with a focus on biomedical applications. More specifically, the book presents a mathematical analysis of basic questions like the well-posedness of the relevant initial and boundary value problems, as well as the modeling and the numerical simulation of a number of fundamental phenomena related to human biology. These latter research topics include blood flow in arteries and veins, blood coagulation and speech modeling. We believe that the variety of the topics discussed, along with the different approaches used to address and solve the corresponding problems, will help readers to develop a more holistic view of the latest findings on the subject, and of the relevant open questions. For the same reason we expect the book to become a trusted companion for researchers from diverse disciplines, such as mathematics, physics, mathematical biology, bioengineering and medicine.

Engineering Approaches to Study Cardiovascular Physiology: Modeling, Estimation, and Signal Processing

Engineering Approaches to Study Cardiovascular Physiology: Modeling, Estimation, and Signal Processing
Author: Riccardo Barbieri
Publisher: Frontiers E-books
Total Pages: 136
Release:
Genre:
ISBN: 288919079X

With cardiovascular diseases being one of the main causes of death in the world, quantitative modeling, assessment and monitoring of the cardiovascular control system plays a critical role in bringing important breakthroughs to cardiovascular care. Quantification of cardiovascular physiology and its control dynamics from physiological recordings and by use of mathematical models and algorithms has been proved to be of important value in understanding the causes of cardiovascular diseases and assisting the prognostic or diagnostic process. Nowadays, development of new recording technologies (e.g., electrophysiology, imaging, ultrasound, etc) has enabled us to improve and expand acquisition of a wide spectrum of physiological measures related to cardiovascular control. An emerging challenge is to process and interpret such increasing amount of information by using state-of-the-art approaches in systems modeling, estimation and control, and signal processing, which would lead to further insightful scientific findings. In particular, multi-disciplinary engineering-empowered approaches of studying cardiovascular systems would greatly deepen our understanding of cardiovascular functions (e.g., heart rate variability, baroreflex sensitivity) and autonomic control, as it would also improve the knowledge about heart pathology, cardiovascular rehabilitation and therapy. Meanwhile, developing cardiovascular biomedical devices or heart-machine interface for either clinical monitoring or rehabilitation purpose is of greater and greater interest for both scientific advancement and potential medical benefits. This Research Topic will bring together established experts whose areas of research cover a wide range of studies and applications. Contributions include but are not limited to state-of-the-art modeling methodologies, algorithmic development in signal processing and estimation, as well as applications in cardiovascular rehabilitation, and clinical monitoring. The Research Topic will consider both invited reviews and original research.

Feedback Systems

Feedback Systems
Author: Karl Johan Åström
Publisher: Princeton University Press
Total Pages:
Release: 2021-02-02
Genre: Technology & Engineering
ISBN: 069121347X

The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory

Advancements in Technology-Based Assessment: Emerging Item Formats, Test Designs, and Data Sources

Advancements in Technology-Based Assessment: Emerging Item Formats, Test Designs, and Data Sources
Author: Frank Goldhammer
Publisher: Frontiers Media SA
Total Pages: 275
Release: 2020-02-20
Genre:
ISBN: 2889635066

This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.