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Approximation Of Large Scale Dynamical Systems
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Book Synopsis Approximation of Large-Scale Dynamical Systems by : Athanasios C. Antoulas
Download or read book Approximation of Large-Scale Dynamical Systems written by Athanasios C. Antoulas and published by SIAM. This book was released on 2009-06-25 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational accuracy and storage capabilities model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications.
Book Synopsis Computational Methods for Approximation of Large-Scale Dynamical Systems by : Mohammad Monir Uddin
Download or read book Computational Methods for Approximation of Large-Scale Dynamical Systems written by Mohammad Monir Uddin and published by CRC Press. This book was released on 2019-04-30 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: These days, computer-based simulation is considered the quintessential approach to exploring new ideas in the different disciplines of science, engineering and technology (SET). To perform simulations, a physical system needs to be modeled using mathematics; these models are often represented by linear time-invariant (LTI) continuous-time (CT) systems. Oftentimes these systems are subject to additional algebraic constraints, leading to first- or second-order differential-algebraic equations (DAEs), otherwise known as descriptor systems. Such large-scale systems generally lead to massive memory requirements and enormous computational complexity, thus restricting frequent simulations, which are required by many applications. To resolve these complexities, the higher-dimensional system may be approximated by a substantially lower-dimensional one through model order reduction (MOR) techniques. Computational Methods for Approximation of Large-Scale Dynamical Systems discusses computational techniques for the MOR of large-scale sparse LTI CT systems. Although the book puts emphasis on the MOR of descriptor systems, it begins by showing and comparing the various MOR techniques for standard systems. The book also discusses the low-rank alternating direction implicit (LR-ADI) iteration and the issues related to solving the Lyapunov equation of large-scale sparse LTI systems to compute the low-rank Gramian factors, which are important components for implementing the Gramian-based MOR. Although this book is primarly aimed at post-graduate students and researchers of the various SET disciplines, the basic contents of this book can be supplemental to the advanced bachelor's-level students as well. It can also serve as an invaluable reference to researchers working in academics and industries alike. Features: Provides an up-to-date, step-by-step guide for its readers. Each chapter develops theories and provides necessary algorithms, worked examples, numerical experiments and related exercises. With the combination of this book and its supplementary materials, the reader gains a sound understanding of the topic. The MATLAB® codes for some selected algorithms are provided in the book. The solutions to the exercise problems, experiment data sets and a digital copy of the software are provided on the book's website; The numerical experiments use real-world data sets obtained from industries and research institutes.
Book Synopsis Interpolatory Methods for Model Reduction by : A. C. Antoulas
Download or read book Interpolatory Methods for Model Reduction written by A. C. Antoulas and published by SIAM. This book was released on 2020-01-13 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.
Book Synopsis Computational Methods for Approximation of Large-Scale Dynamical Systems by : Mohammad Monir Uddin
Download or read book Computational Methods for Approximation of Large-Scale Dynamical Systems written by Mohammad Monir Uddin and published by CRC Press. This book was released on 2019-04-30 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: These days, computer-based simulation is considered the quintessential approach to exploring new ideas in the different disciplines of science, engineering and technology (SET). To perform simulations, a physical system needs to be modeled using mathematics; these models are often represented by linear time-invariant (LTI) continuous-time (CT) systems. Oftentimes these systems are subject to additional algebraic constraints, leading to first- or second-order differential-algebraic equations (DAEs), otherwise known as descriptor systems. Such large-scale systems generally lead to massive memory requirements and enormous computational complexity, thus restricting frequent simulations, which are required by many applications. To resolve these complexities, the higher-dimensional system may be approximated by a substantially lower-dimensional one through model order reduction (MOR) techniques. Computational Methods for Approximation of Large-Scale Dynamical Systems discusses computational techniques for the MOR of large-scale sparse LTI CT systems. Although the book puts emphasis on the MOR of descriptor systems, it begins by showing and comparing the various MOR techniques for standard systems. The book also discusses the low-rank alternating direction implicit (LR-ADI) iteration and the issues related to solving the Lyapunov equation of large-scale sparse LTI systems to compute the low-rank Gramian factors, which are important components for implementing the Gramian-based MOR. Although this book is primarly aimed at post-graduate students and researchers of the various SET disciplines, the basic contents of this book can be supplemental to the advanced bachelor's-level students as well. It can also serve as an invaluable reference to researchers working in academics and industries alike. Features: Provides an up-to-date, step-by-step guide for its readers. Each chapter develops theories and provides necessary algorithms, worked examples, numerical experiments and related exercises. With the combination of this book and its supplementary materials, the reader gains a sound understanding of the topic. The MATLAB® codes for some selected algorithms are provided in the book. The solutions to the exercise problems, experiment data sets and a digital copy of the software are provided on the book's website; The numerical experiments use real-world data sets obtained from industries and research institutes.
Book Synopsis Differential Dynamical Systems, Revised Edition by : James D. Meiss
Download or read book Differential Dynamical Systems, Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.
Book Synopsis Dimension Reduction of Large-Scale Systems by : Peter Benner
Download or read book Dimension Reduction of Large-Scale Systems written by Peter Benner and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.
Book Synopsis Multi-Resolution Methods for Modeling and Control of Dynamical Systems by : Puneet Singla
Download or read book Multi-Resolution Methods for Modeling and Control of Dynamical Systems written by Puneet Singla and published by CRC Press. This book was released on 2008-08-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unifying the most important methodology in this field, Multi-Resolution Methods for Modeling and Control of Dynamical Systems explores existing approximation methods as well as develops new ones for the approximate solution of large-scale dynamical system problems. It brings together a wide set of material from classical orthogonal function approximation, neural network input-output approximation, finite element methods for distributed parameter systems, and various approximation methods employed in adaptive control and learning theory. With sufficient rigor and generality, the book promotes a qualitative understanding of the development of key ideas. It facilitates a deep appreciation of the important nuances and restrictions implicit in the algorithms that affect the validity of the results produced. The text features benchmark problems throughout to offer insights and illustrate some of the computational implications. The authors provide a framework for understanding the advantages, drawbacks, and application areas of existing and new algorithms for input-output approximation. They also present novel adaptive learning algorithms that can be adjusted in real time to the various parameters of unknown mathematical models.
Author :Wilhelmus H. Schilders Publisher :Springer Science & Business Media ISBN 13 :3540788417 Total Pages :471 pages Book Rating :4.5/5 (47 download)
Book Synopsis Model Order Reduction: Theory, Research Aspects and Applications by : Wilhelmus H. Schilders
Download or read book Model Order Reduction: Theory, Research Aspects and Applications written by Wilhelmus H. Schilders and published by Springer Science & Business Media. This book was released on 2008-08-27 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.
Book Synopsis Approximate Dynamic Programming by : Warren B. Powell
Download or read book Approximate Dynamic Programming written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2007-10-05 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete and accessible introduction to the real-world applications of approximate dynamic programming With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines—Markov design processes, mathematical programming, simulation, and statistics—to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems. Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues. With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming: Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts.
Book Synopsis Mathematical Models by : Richard Haberman
Download or read book Mathematical Models written by Richard Haberman and published by SIAM. This book was released on 1998-12-01 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author uses mathematical techniques to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow.
Book Synopsis The Mathematics Of Large-scale Atmosphere And Ocean by : Michael John Priestley Cullen
Download or read book The Mathematics Of Large-scale Atmosphere And Ocean written by Michael John Priestley Cullen and published by World Scientific. This book was released on 2021-06-04 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The high predictability of the atmosphere and ocean depends on the existence of a 'slow manifold', which contains the solutions of equations describing only large-scale motions. This unique compendium succinctly describes major recent advances in showing that these equations can be solved independently.The book is a new edition of a similar book published 15 years ago. The explanation of the mathematical techniques has been expanded. Many new theoretical results are included. Illustrations derived from production atmosphere and ocean models are also incorporated to cover the full range between rigorous mathematics and state-of-the-art numerical modelling.The author is a dynamical meteorologist with long experience and international standing. The mathematical results in the book were proved by many of the world's leading analysts. The results come from the Met Office Unified Model, which is one of the world's leading weather and climate models.Related Link(s)
Book Synopsis Invitation to Dynamical Systems by : Edward R. Scheinerman
Download or read book Invitation to Dynamical Systems written by Edward R. Scheinerman and published by Courier Corporation. This book was released on 2013-05-13 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.
Book Synopsis Navier-Stokes Equations and Nonlinear Functional Analysis by : Roger Temam
Download or read book Navier-Stokes Equations and Nonlinear Functional Analysis written by Roger Temam and published by SIAM. This book was released on 1995-01-01 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations.
Book Synopsis Stability and Control of Large-Scale Dynamical Systems by : Wassim M. Haddad
Download or read book Stability and Control of Large-Scale Dynamical Systems written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2011-12-04 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of technological, environmental, and social phenomena. This book develops stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems.
Book Synopsis Dynamical Systems and Numerical Analysis by : Andrew Stuart
Download or read book Dynamical Systems and Numerical Analysis written by Andrew Stuart and published by Cambridge University Press. This book was released on 1998-11-28 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.
Book Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd
Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Book Synopsis Large Scale Matrix Problems by : Åke Björck
Download or read book Large Scale Matrix Problems written by Åke Björck and published by North-Holland. This book was released on 1981 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
