The Riccati Equation
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| Author | : Sergio Bittanti |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 346 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 3642582230 |
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 |
| Publisher | : Birkhäuser |
| Total Pages | : 584 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3034880812 |
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 | : Reid |
| Publisher | : Academic Press |
| Total Pages | : 227 |
| Release | : 1972-08-22 |
| Genre | : Computers |
| ISBN | : 0080955959 |
Riccati Differential Equations
| Author | : Dario A. Bini |
| Publisher | : SIAM |
| Total Pages | : 261 |
| Release | : 2012-03-31 |
| Genre | : Mathematics |
| ISBN | : 1611972086 |
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 | : Peter Lancaster |
| Publisher | : Clarendon Press |
| Total Pages | : 502 |
| Release | : 1995-09-07 |
| Genre | : Mathematics |
| ISBN | : 0191591254 |
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 | : Aleksandr Ivanovič Egorov |
| Publisher | : Pensoft Publishers |
| Total Pages | : 390 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9789546422965 |
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 | : M.I. Zelikin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 3662041367 |
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 | : Serafin Fraga |
| Publisher | : Springer |
| Total Pages | : 248 |
| Release | : 1999 |
| Genre | : Computers |
| ISBN | : |
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 | : I. I. Kolodner |
| Publisher | : |
| Total Pages | : 36 |
| Release | : 1962 |
| Genre | : Differential equations |
| ISBN | : |
| Author | : Dieter Schuch |
| Publisher | : Springer |
| Total Pages | : 261 |
| Release | : 2018-01-20 |
| Genre | : Science |
| ISBN | : 3319655949 |
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.
