The Riccati Equation

Author : Sergio Bittanti,Alan J. Laub,Jan C. Willems
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642582233

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The Riccati Equation by Sergio Bittanti,Alan J. Laub,Jan C. Willems Pdf

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.

Author : Hisham Abou-Kandil,Gerhard Freiling,Vlad Ionescu,Gerhard Jank
Publisher : Birkhäuser
Page : 584 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034880817

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Matrix Riccati Equations in Control and Systems Theory by Hisham Abou-Kandil,Gerhard Freiling,Vlad Ionescu,Gerhard Jank Pdf

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.

Author : Peter Lancaster,Leiba Rodman
Publisher : Clarendon Press
Page : 502 pages
File Size : 46,8 Mb
Release : 1995-09-07
Category : Mathematics
ISBN : 9780191591259

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Algebraic Riccati Equations by Peter Lancaster,Leiba Rodman Pdf

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.

Author : Serafin Fraga,José Manuel García de la Vega,Eric S. Fraga
Publisher : Springer
Page : 248 pages
File Size : 43,5 Mb
Release : 1999
Category : Computers
ISBN : UOM:39015057383302

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The Schrödinger and Riccati Equations by Serafin Fraga,José Manuel García de la Vega,Eric S. Fraga Pdf

The linear Schrödinger equation is central to Quantum Chemistry. It is presented within the context of relativistic Quantum Mechanics and analysed both in time-dependent and time-independent forms. The Riccati equation is used to study the one-dimensional Schrödinger equation. The authors develop the Schrödinger-Riccati equation as an approach to determine solutions of the time-independent, linear Schrödinger equation.

Author : Aleksandr Ivanovič Egorov
Publisher : Pensoft Publishers
Page : 390 pages
File Size : 51,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9546422967

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Riccati Equations by Aleksandr Ivanovič Egorov Pdf

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.

Author : Dieter Schuch
Publisher : Springer
Page : 258 pages
File Size : 49,6 Mb
Release : 2018-01-20
Category : Science
ISBN : 9783319655949

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Quantum Theory from a Nonlinear Perspective by Dieter Schuch Pdf

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.

Author : Dario A. Bini,Bruno Iannazzo,Beatrice Meini
Publisher : SIAM
Page : 261 pages
File Size : 50,9 Mb
Release : 2012-03-31
Category : Mathematics
ISBN : 9781611972085

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Numerical Solution of Algebraic Riccati Equations by Dario A. Bini,Bruno Iannazzo,Beatrice Meini Pdf

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.

Author : Reid
Publisher : Academic Press
Page : 215 pages
File Size : 48,7 Mb
Release : 1972-08-22
Category : Mathematics
ISBN : 9780080955957

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Riccati Differential Equations by Reid Pdf

Riccati Differential Equations

Author : M.I. Zelikin
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 46,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662041369

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Control Theory and Optimization I by M.I. Zelikin Pdf

The only monograph on the topic, this book concerns geometric methods in the theory of differential equations with quadratic right-hand sides, closely related to the calculus of variations and optimal control theory. Based on the author’s lectures, the book is addressed to undergraduate and graduate students, and scientific researchers.

Author : I. I. Kolodner,Joseph Lehner,George Milton Wing
Publisher : Unknown
Page : 36 pages
File Size : 41,6 Mb
Release : 1962
Category : Differential equations
ISBN : UOM:39015095052596

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On Riccati and Riccati-like Equations Arising in One-dimensional Diffusion Problems by I. I. Kolodner,Joseph Lehner,George Milton Wing Pdf

Author : Irena Lasiecka,Roberto Triggiani
Publisher : Springer
Page : 184 pages
File Size : 40,6 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015024896089

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Differential and Algebraic Riccati Equations with Application to Boundary/point Control Problems by Irena Lasiecka,Roberto Triggiani Pdf

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.

Author : Calvin Ahlbrandt,A.C. Peterson
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 44,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475724677

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Discrete Hamiltonian Systems by Calvin Ahlbrandt,A.C. Peterson Pdf

This book should be accessible to students who have had a first course in matrix theory. The existence and uniqueness theorem of Chapter 4 requires the implicit function theorem, but we give a self-contained constructive proof ofthat theorem. The reader willing to accept the implicit function theorem can read the book without an advanced calculus background. Chapter 8 uses the Moore-Penrose pseudo-inverse, but is accessible to students who have facility with matrices. Exercises are placed at those points in the text where they are relevant. For U. S. universities, we intend for the book to be used at the senior undergraduate level or beginning graduate level. Chapter 2, which is on continued fractions, is not essential to the material of the remaining chapters, but is intimately related to the remaining material. Continued fractions provide closed form representations of the extreme solutions of some discrete matrix Riccati equations. Continued fractions solution methods for Riccati difference equations provide an approach analogous to series solution methods for linear differential equations. The book develops several topics which have not been available at this level. In particular, the material of the chapters on continued fractions (Chapter 2), symplectic systems (Chapter 3), and discrete variational theory (Chapter 4) summarize recent literature. Similarly, the material on transforming Riccati equations presented in Chapter 3 gives a self-contained unification of various forms of Riccati equations. Motivation for our approach to difference equations came from the work of Harris, Vaughan, Hartman, Reid, Patula, Hooker, Erbe & Van, and Bohner.

Author : E. P. Merkes,William T. Scott
Publisher : Unknown
Page : 44 pages
File Size : 49,8 Mb
Release : 1961
Category : Riccati equation
ISBN : UOM:39015095249762

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Continued Fraction Solutions of the Riccati Equation by E. P. Merkes,William T. Scott Pdf

Author : Peter Lancaster,L. Rodman
Publisher : Unknown
Page : 0 pages
File Size : 50,6 Mb
Release : 2023
Category : Riccati equation
ISBN : 1383026297

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Algebraic Riccati Equations by Peter Lancaster,L. Rodman Pdf

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.

Author : Gerhard Jank
Publisher : Unknown
Page : 122 pages
File Size : 47,9 Mb
Release : 2005
Category : Differential equations
ISBN : UOM:39015069163478

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Matrix Riccati Differential Equations by Gerhard Jank Pdf