Numerical Solution of Algebraic Riccati Equations
Numerical Solution of Algebraic Riccati Equations

Author: Dario A. Bini

Publisher: SIAM

Published: 2012-03-31

Total Pages: 261

ISBN-13: 1611972086

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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.

Numerical Solution of Algebraic Riccati Equations
Numerical Solution of Algebraic Riccati Equations

Author: Dario A. Bini

Publisher: SIAM

Published: 2011-01-01

Total Pages: 266

ISBN-13: 9781611972092

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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.

The Riccati Equation
The Riccati Equation

Author: Sergio Bittanti

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 346

ISBN-13: 3642582230

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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.

Numerical Solution of Initial-value Problems in Differential-algebraic Equations
Numerical Solution of Initial-value Problems in Differential-algebraic Equations

Author: K. E. Brenan

Publisher: SIAM

Published: 1996-01-01

Total Pages: 268

ISBN-13: 9781611971224

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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
Algebraic Riccati Equations

Author: Peter Lancaster

Publisher: Clarendon Press

Published: 1995-09-07

Total Pages: 502

ISBN-13: 0191591254

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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 Autonomous Linear Quadratic Control Problem
The Autonomous Linear Quadratic Control Problem

Author: Volker L. Mehrmann

Publisher: Lecture Notes in Control and Information Sciences

Published: 1991

Total Pages: 192

ISBN-13:

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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.

Analytical and Numerical Methods for Volterra Equations
Analytical and Numerical Methods for Volterra Equations

Author: Peter Linz

Publisher: SIAM

Published: 1985-01-01

Total Pages: 240

ISBN-13: 9781611970852

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Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.

Numerical Methods for Linear Control Systems
Numerical Methods for Linear Control Systems

Author: Biswa Datta

Publisher: Elsevier

Published: 2004-02-24

Total Pages: 736

ISBN-13: 008053788X

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Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. - Unique coverage of modern mathematical concepts such as parallel computations, second-order systems, and large-scale solutions - Background material in linear algebra, numerical linear algebra, and control theory included in text - Step-by-step explanations of the algorithms and examples