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Author : Reid
Publisher : Academic Press
Page : 215 pages
File Size : 52,8 Mb
Release : 1972-08-22
Category : Mathematics
ISBN : 9780080955957
Riccati Differential Equations
Author : Sergio Bittanti,Alan J. Laub,Jan C. Willems
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642582233
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 : 55,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034880817
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 : Aleksandr Ivanovič Egorov
Publisher : Pensoft Publishers
Page : 390 pages
File Size : 45,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9546422967
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 : Gerhard Jank
Publisher : Unknown
Page : 122 pages
File Size : 45,6 Mb
Release : 2005
Category : Differential equations
ISBN : UOM:39015069163478
Author : William Thomas Reid
Publisher : Unknown
Page : 58 pages
File Size : 52,8 Mb
Release : 1959
Category : Differential equations
ISBN : UOM:39015095251107
Author : Ondrej Dosly,Pavel Rehak
Publisher : Elsevier
Page : 533 pages
File Size : 53,7 Mb
Release : 2005-07-06
Category : Mathematics
ISBN : 9780080461236
The book presents a systematic and compact treatment of the qualitative theory of half-linear differential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE’s with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations. - The first complete treatment of the qualitative theory of half-linear differential equations. - Comparison of linear and half-linear theory. - Systematic approach to half-linear oscillation and asymptotic theory. - Comprehensive bibliography and index. - Useful as a reference book in the topic.
Author : I. I. Kolodner,Joseph Lehner,George Milton Wing
Publisher : Unknown
Page : 36 pages
File Size : 43,5 Mb
Release : 1962
Category : Differential equations
ISBN : UOM:39015095052596
Author : Irena Lasiecka,Roberto Triggiani
Publisher : Springer
Page : 184 pages
File Size : 47,5 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015024896089
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 : William Thomas Reid
Publisher : Unknown
Page : 240 pages
File Size : 53,7 Mb
Release : 1972
Category : Differential equations
ISBN : UOM:39015000979230
Author : Valentin F. Zaitsev,Andrei D. Polyanin
Publisher : CRC Press
Page : 815 pages
File Size : 41,8 Mb
Release : 2002-10-28
Category : Mathematics
ISBN : 9781420035339
Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handboo
Author : Dario A. Bini,Bruno Iannazzo,Beatrice Meini
Publisher : SIAM
Page : 261 pages
File Size : 52,6 Mb
Release : 2012-03-31
Category : Mathematics
ISBN : 9781611972085
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 : Dieter Schuch
Publisher : Springer
Page : 258 pages
File Size : 52,5 Mb
Release : 2018-01-20
Category : Science
ISBN : 9783319655949
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 : Peter Lancaster,Leiba Rodman
Publisher : Clarendon Press
Page : 502 pages
File Size : 45,7 Mb
Release : 1995-09-07
Category : Mathematics
ISBN : 9780191591259
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 : Milton Abramowitz,Irene A. Stegun
Publisher : Courier Corporation
Page : 1068 pages
File Size : 46,9 Mb
Release : 1965-01-01
Category : Mathematics
ISBN : 0486612724
An extensive summary of mathematical functions that occur in physical and engineering problems