Numerical Solution of Algebraic Riccati Equations

Author: Dario A. Bini,Bruno Iannazzo,Beatrice Meini

Publisher: SIAM

ISBN: 1611972086

Category: Mathematics

Page: 250

View: 866

This treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practitioners and scholars. It is the first book in which nonsymmetric algebraic Riccati equations are treated in a clear and systematic way. Some proofs of theoretical results have been simplified and a unified notation has been adopted. Readers will find a unified discussion of doubling algorithms, which are effective in solving algebraic Riccati equations as well as a detailed description of all classical and advanced algorithms for solving algebraic Riccati equations and their MATLAB codes. This will help the reader gain an understanding of the computational issues and provide ready-to-use implementation of the different solution techniques.
Posted in Mathematics

Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

Festschrift in Honor of Volker Mehrmann

Author: Peter Benner,Matthias Bollhöfer,Daniel Kressner,Christian Mehl,Tatjana Stykel

Publisher: Springer

ISBN: 3319152602

Category: Mathematics

Page: 608

View: 701

This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.
Posted in Mathematics

Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications

Cetraro, Italy 2015

Author: Michele Benzi,Dario Bini,Daniel Kressner,Hans Munthe-Kaas,Charles Van Loan

Publisher: Springer

ISBN: 3319498878

Category: Mathematics

Page: 406

View: 8684

Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.
Posted in Mathematics

Numerical Analysis of Partial Differential Equations Using Maple and MATLAB

Author: Martin J. Gander,Felix Kwok

Publisher: SIAM

ISBN: 1611975301

Category: Science

Page: N.A

View: 2461

This book provides an elementary yet comprehensive introduction to the numerical solution of partial differential equations (PDEs). Used to model important phenomena, such as the heating of apartments and the behavior of electromagnetic waves, these equations have applications in engineering and the life sciences, and most can only be solved approximately using computers. Numerical Analysis of Partial Differential Equations Using Maple and MATLAB provides detailed descriptions of the four major classes of discretization methods for PDEs (finite difference method, finite volume method, spectral method, and finite element method) and runnable MATLAB® code for each of the discretization methods and exercises. It also gives self-contained convergence proofs for each method using the tools and techniques required for the general convergence analysis but adapted to the simplest setting to keep the presentation clear and complete. This book is intended for advanced undergraduate and early graduate students in numerical analysis and scientific computing and researchers in related fields. It is appropriate for a course on numerical methods for partial differential equations.
Posted in Science

Fundamental Numerical Methods for Electrical Engineering

Author: Stanislaw Rosloniec

Publisher: Springer Science & Business Media

ISBN: 3540795197

Category: Technology & Engineering

Page: 284

View: 4134

Stormy development of electronic computation techniques (computer systems and software), observed during the last decades, has made possible automation of data processing in many important human activity areas, such as science, technology, economics and labor organization. In a broadly understood technology area, this developmentledtoseparationofspecializedformsofusingcomputersforthedesign and manufacturing processes, that is: – computer-aided design (CAD) – computer-aided manufacture (CAM) In order to show the role of computer in the rst of the two applications m- tioned above, let us consider basic stages of the design process for a standard piece of electronic system, or equipment: – formulation of requirements concerning user properties (characteristics, para- ters) of the designed equipment, – elaboration of the initial, possibly general electric structure, – determination of mathematical model of the system on the basis of the adopted electric structure, – determination of basic responses (frequency- or time-domain) of the system, on the base of previously established mathematical model, – repeated modi cation of the adopted diagram (changing its structure or element values) in case, when it does not satisfy the adopted requirements, – preparation of design and technological documentation, – manufacturing of model (prototype) series, according to the prepared docum- tation, – testing the prototype under the aspect of its electric properties, mechanical du- bility and sensitivity to environment conditions, – modi cation of prototype documentation, if necessary, and handing over the documentation to series production. The most important stages of the process under discussion are illustrated in Fig. I. 1. xi xii Introduction Fig. I.
Posted in Technology & Engineering

Matrix Riccati Equations in Control and Systems Theory

Author: Hisham Abou-Kandil,Gerhard Freiling,Vlad Ionescu,Gerhard Jank

Publisher: Springer Science & Business Media

ISBN: 9783764300852

Category: Science

Page: 572

View: 4303

The authors present the theory of symmetric (Hermitian) matrix Riccati equations and contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach. The book makes available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.
Posted in Science

Computational Matrix Analysis

Author: Alan J. Laub

Publisher: SIAM

ISBN: 9781611972214

Category: Matrix analytic methods

Page: 156

View: 5905

Using an approach that author Alan Laub calls "matrix analysis for grown-ups," this new textbook introduces fundamental concepts of numerical linear algebra and their application to solving certain numerical problems arising in state-space control and systems theory. It is written for advanced undergraduate and beginning graduate students and can be used as a follow-up to Matrix Analysis for Scientists and Engineers (SIAM, 2005), a compact single-semester introduction to matrix analysis for engineers and computational scientists by the same author. Computational Matrix Analysis provides readers with a one-semester introduction to numerical linear algebra; an introduction to statistical condition estimation in book form for the first time; and an overview of certain computational problems in control and systems theory. The book features a number of elements designed to help students learn to use numerical linear algebra in day-to-day computing or research, including a brief review of matrix analysis, including notation, and an introduction to finite (IEEE) arithmetic; discussion and examples of conditioning, stability, and rounding analysis; an introduction to mathematical software topics related to numerical linear algebra; a thorough introduction to Gaussian elimination, along with condition estimation techniques; coverage of linear least squares, with orthogonal reduction and QR factorization; variants of the QR algorithm; and applications of the discussed algorithms.
Posted in Matrix analytic methods

Lyapunov Matrix Equation in System Stability and Control

Author: Zoran Gajic,Muhammad Tahir Javed Qureshi

Publisher: Elsevier

ISBN: 9780080535678

Category: Mathematics

Page: 255

View: 7918

The Lyapunov and Riccati equations are two of the fundamental equations of control and system theory, having special relevance for system identification, optimization, boundary value problems, power systems, signal processing, and communications. The Lyapunov Matrix Equation in System Stability and Control covers mathematical developments and applications while providing quick and easy references for solutions to engineering and mathematical problems. Examples of real-world systems are given throughout the text in order to demonstrate the effectiveness of the presented methods and algorithms. The book will appeal to practicing engineers, theoreticians, applied mathematicians, and graduate students who seek a comprehensive view of the main results of the Lyapunov matrix equation. Presents techniques for solving and analyzing the algebraic, differential, and difference Lyapunov matrix equations of continuous-time and discrete-time systems Offers summaries and references at the end of each chapter Contains examples of the use of the equation to solve real-world problems Provides quick and easy references for the solutions to engineering and mathematical problems using the Lyapunov equation
Posted in Mathematics

Proceedings of the 1978 IEEE Conference on Decision & Control

including the 17th Symposium on Adaptive Processes, January 10-12, 1979, Islandia Hyatt House Hotel, San Diego, California

Author: Institute of Electrical and Electronics Engineers,IEEE Control Systems Society

Publisher: N.A

ISBN: N.A

Category: Education

Page: 1461

View: 3796

Posted in Education

Kalman-Bucy-Filter

Deterministische Beobachtung und stochastische Filterung

Author: Karl Brammer,Gerhard Siffling

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486785524

Category: Science

Page: 232

View: 9417

Das Buch führt den Leser auf elementarem Wege in die Wahrscheinlichkeitsrechnung und in die Theorie der Zufallsprozesse ein, wobei keinerlei Vorkenntnisse auf diesem Gebiet vorausgesetzt werden. Schließlich wird gezeigt, wie sich die Eigenschaften eines Zufallsprozesses bei der Übertragung durch ein lineares System verändern und wie diese veränderten Eigenschaften berechnet werden können.
Posted in Science

Neural networks

a comprehensive foundation

Author: Simon S. Haykin

Publisher: Macmillan ; Toronto : Maxwell Macmillan Canada

ISBN: 9780023527616

Category: Computers

Page: 696

View: 1780

This book represents the most comprehensive treatment available of neural networks from an engineering perspective. Thorough, well-organized, and completely up to date, it examines all the important aspects of this emerging technology, including the learning process, back-propagation learning, radial-basis function networks, self-organizing systems, modular networks, temporal processing and neurodynamics, and VLSI implementation of neural networks. Written in a concise and fluid manner, by a foremost engineering textbook author, to make the material more accessible, this book is ideal for professional engineers and graduate students entering this exciting field. Computer experiments, problems, worked examples, a bibliography, photographs, and illustrations reinforce key concepts.
Posted in Computers

Polynomial Methods in Optimal Control and Filtering

Author: Kenneth J. Hunt

Publisher: IET

ISBN: 9780863412950

Category: Technology & Engineering

Page: 309

View: 8295

This book aims to demonstrate the power and breadth of polynomial methods in the control of engineering systems and the filtering of signals. Using commissioned contributions from renowned international specialists, the book progresses logically from the necessary background material (given at a tutorial level), through recent theoretical and practical developments, to detailed presentation of numerical algorithms. Includes: algebraic approach to control system design; LQ-controller design and and self-tuning control; optimal filtering problems; n-D polynomial equations; polynomial equations; conjugacy and symmetry; J-spectral factorisation.
Posted in Technology & Engineering

Proceedings of the 24th IEEE Conference on Decision & Control

December 11-13, 1985, Bonaventure Hotel & Spa, Fort Lauderdale, Florida

Author: IEEE Control Systems Society,Institute of Electrical and Electronics Engineers

Publisher: N.A

ISBN: N.A

Category: Adaptive control systems

Page: 2060

View: 9177

Posted in Adaptive control systems

Practical Applications of Parallel Computing

Author: Laurence Tianruo Yang,Marcin Paprzycki

Publisher: New York : Nova Science Publishers

ISBN: N.A

Category: Computers

Page: 414

View: 812

The continuous progress in scientific research is one of the important factors explaining the constantly increasing demand for computational power. On the other hand, one of the results of such progress is the availability of more powerful computer platforms. To that end, this volume reviews a broad array of subjects based on the solutions to the daily problems in industrial production, research, and development.
Posted in Computers

Computer-aided control systems engineering

Author: Mohammad Jamshidi

Publisher: North Holland

ISBN: N.A

Category: Technology & Engineering

Page: 384

View: 7222

Posted in Technology & Engineering

Hierarchische Matrizen

Algorithmen und Analysis

Author: Wolfgang Hackbusch

Publisher: Springer Science & Business Media

ISBN: 3642002218

Category: Mathematics

Page: 451

View: 828

Bei der Diskretisierung von Randwertaufgaben und Integralgleichungen entstehen große, eventuell auch voll besetzte Matrizen. In dem Band stellt der Autor eine neuartige Methode dar, die es erstmals erlaubt, solche Matrizen nicht nur effizient zu speichern, sondern auch alle Matrixoperationen einschließlich der Matrixinversion bzw. der Dreieckszerlegung approximativ durchzuführen. Anwendung findet diese Technik nicht nur bei der Lösung großer Gleichungssysteme, sondern auch bei Matrixgleichungen und der Berechnung von Matrixfunktionen.
Posted in Mathematics

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6556

Posted in Mathematics