Numerical Solution Of Algebraic Riccati Equations
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Numerical Solution Of Algebraic Riccati Equations
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Author : Dario A. Bini
language : en
Publisher: SIAM
Release Date : 2012-03-31
Numerical Solution Of Algebraic Riccati Equations written by Dario A. Bini and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-31 with Mathematics categories.
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.
Contributions To The Numerical Solution Of Algebraic Riccati Equations And Related Eigenvalue Problems
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Author : Peter Benner
language : en
Publisher:
Release Date : 1997
Contributions To The Numerical Solution Of Algebraic Riccati Equations And Related Eigenvalue Problems written by Peter Benner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Eigenvalues categories.
Algebraic Riccati Equations
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Author : Peter Lancaster
language : en
Publisher: Clarendon Press
Release Date : 1995-09-07
Algebraic Riccati Equations written by Peter Lancaster and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-07 with Mathematics categories.
This book provides a careful treatment of the theory of algebraic Riccati equations. It consists of four parts: the first part is a comprehensive account of necessary background material in matrix theory including careful accounts of recent developments involving indefinite scalar products and rational matrix functions. The second and third parts form the core of the book and concern the solutions of algebraic Riccati equations arising from continuous and discrete systems. The geometric theory and iterative analysis are both developed in detail. The last part of the book is an exciting collection of eight problem areas in which algebraic Riccati equations play a crucial role. These applications range from introductions to the classical linear quadratic regulator problems and the discrete Kalman filter to modern developments in HD*W*w control and total least squares methods.
The Riccati Equation
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Author : Sergio Bittanti
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Riccati Equation written by Sergio Bittanti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
Conceived by Count Jacopo Francesco Riccati more than a quarter of a millennium ago, the Riccati equation has been widely studied in the subsequent centuries. Since its introduction in control theory in the sixties, the matrix Riccati equation has known an impressive range of applications, such as optimal control, H? optimization and robust stabilization, stochastic realization, synthesis of linear passive networks, to name but a few. This book consists of 11 chapters surveying the main concepts and results related to the matrix Riccati equation, both in continuous and discrete time. Theory, applications and numerical algorithms are extensively presented in an expository way. As a foreword, the history and prehistory of the Riccati equation is concisely presented.
The Autonomous Linear Quadratic Control Problem
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Author : Volker L. Mehrmann
language : en
Publisher: Lecture Notes in Control and Information Sciences
Release Date : 1991
The Autonomous Linear Quadratic Control Problem written by Volker L. Mehrmann and has been published by Lecture Notes in Control and Information Sciences this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Language Arts & Disciplines categories.
A survey is given on the state of the art in theory and numerical solution of general autonomous linear quadratic optimal control problems (continuous and discrete) with differential algebraic equation constraints. It incorporates the newest developments on differential algebraic equations, Riccati equations and invariant subspace problems. In particular, it gives a decision chart of numerical methods, that can be used to determine the right numerical method according to special properties of the problem. The book closes a gap between mathematical theory, numerical solution and engineering application. The mathematical tools are kept as basic as possible in order to address the different groups of readers, mathematicians and engineers.
Differential And Algebraic Riccati Equations With Application To Boundary Point Control Problems
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Author : Irena Lasiecka
language : en
Publisher: Springer
Release Date : 1991
Differential And Algebraic Riccati Equations With Application To Boundary Point Control Problems written by Irena Lasiecka and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This book provides, in a unified framework, an updated and rather comprehensive treatment contered on the theory of ot- pimal control with quadratic cost functional for abstract linear systems with application to boundary/point control problems for partial differential equations (distributed pa- rameter systems). The book culminates with the analysisof differential and algebraic Riccati equations which arise in the pointwisefe- edback synthesis of the optimal pair. It incorporates the critical topics of optimal irregularity of solutions to mi- xed problems for partial differential equations, exact con- trollability, and uniform feedback stabilization. It covers the main results of the theory - which has reached a consi- derable degree of maturity over the last few years - as well asthe authors' basic philosophy behind it. Moreover, it provides numerous illustrative examples of boundary/point control problems for partial differential equations, where the abstract theory applies. However, in line with the purpose of the manuscript, many technical pro- ofs are referred to in the literature. Thus, the manuscript should prove useful not only to mathematicians and theoreti- cal scientists with expertise in partial differential equa- tions, operator theory, numerical analysis, control theory, etc., but also to those who simple wish to orient themselves with the scope and status of the theory presently available. Both continuous theory and numerical approximation theory thereof are included.
Riccati Equations
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Author : Aleksandr Ivanovič Egorov
language : en
Publisher: Pensoft Publishers
Release Date : 2007
Riccati Equations written by Aleksandr Ivanovič Egorov and has been published by Pensoft Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Presents the necessary auxiliary facts from algebra, functional analysis and Lie group analysis. This book illustrates theory with solutions of numerous examples. It also presents the matrix Riccati equations. It deals with theoretical questions concerning matrix and operator equations based on various applied problems from mathematical physics.
Numerical Solution Of Initial Value Problems In Differential Algebraic Equations
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Author : K. E. Brenan
language : en
Publisher: SIAM
Release Date : 1996-01-01
Numerical Solution Of Initial Value Problems In Differential Algebraic Equations written by K. E. Brenan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. This classic edition, originally published in 1989, is the only general DAE book available. It not only develops guidelines for choosing different numerical methods, it is the first book to discuss DAE codes, including the popular DASSL code. An extensive discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAE's. New to this edition is a chapter that brings the discussion of DAE software up to date. The objective of this monograph is to advance and consolidate the existing research results for the numerical solution of DAE's. The authors present results on the analysis of numerical methods, and also show how these results are relevant for the solution of problems from applications. They develop guidelines for problem formulation and effective use of the available mathematical software and provide extensive references for further study.
Algebraic Riccati Equations
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Author : Peter Lancaster
language : en
Publisher:
Release Date : 2023
Algebraic Riccati Equations written by Peter Lancaster and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Riccati equation categories.
This monograph provides a treatment of the theory of algebraic Riccati equations, an area of increasing interest in the mathematics and engineering communities. A range of applications are covered, demonstrating the use of these equations for providing solutions to complex problems.
Numerical Algebra Matrix Theory Differential Algebraic Equations And Control Theory
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Author : Peter Benner
language : en
Publisher: Springer
Release Date : 2015-05-09
Numerical Algebra Matrix Theory Differential Algebraic Equations And Control Theory written by Peter Benner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-09 with Mathematics categories.
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.