Last edited by Shaktigami
Friday, May 15, 2020 | History

5 edition of Matrix Riccati Equations found in the catalog.

Matrix Riccati Equations

H. Abou-Kandil

# Matrix Riccati Equations

## by H. Abou-Kandil

Written in English

Subjects:
• Differential Equations,
• Mathematics,
• Riccati equation,
• Control theory,
• Science/Mathematics

• The Physical Object
FormatHardcover
ID Numbers
Open LibraryOL9581456M
ISBN 10081760085X
ISBN 109780817600853
OCLC/WorldCa52688085

The research reported in this book was supported in part by AFOSR (under FJ),NSF(underECS),andARPA(underF). eresupportedinpartbytheDelegation Gen erale pourFile Size: 1MB. The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process.

Matrix difference equation explained. A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. The order of the equation is the maximum time gap between any two indicated values of the variable vector. Buy Riccati Equations (): NHBS - AI Egorov, Pensoft Publishers.

The book can be used in a semester course on algebraic Riccati equations or as a reference in a course on advanced numerical linear algebra and applications. Topics include matrix equations, nonsymmetric equations, concepts and deﬁnitions, and invariant subspaces and algebraic Riccati equations. The book can be used in a semester course on algebraic Riccati equations or as a reference in a course on advanced numerical linear algebra and applications. Cited By Lin M and Chiang C () An accelerated technique for solving one type of discrete-time algebraic Riccati equations, Journal of Computational and Applied Mathematics, C.

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Matrix Riccati Equations arise frequently in applied mathematics, science, and engineering problems. These nonlinear matrix equations are particularly significant in optimal control, filtering, and estimation problems.

Essentially, solving a Riccati Cited by: 4. The aim of the book is to present the state of the art of the theory of symmetric (Hermitian) matrix Riccati equations and to 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.

from book Matrix Riccati Equations in Control and Systems Theory (pp) Matrix Matrix Riccati Equations book Equations in Control and Systems Theory Chapter January with 42 Reads.

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 Cited by: "The aim of the book is to present the state of the art of the theory of symmetric (Hermitian) matrix Riccati equations and to 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.

This book provides a careful treatment of the theory Matrix Riccati Equations book 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 aim of the book is to present the state of the art of the theory of symmetric (Hermitian) matrix Riccati equations and to 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. In this book, scalar, matrix and operator Riccati equations are considered.

Theoretical questions and practical methods of solution of these equations are expounded. The necessary auxiliary facts from algebra, functional analysis and Lie group analysis are given. Theory is illustrated with solutions of numerous : A.

Egorov. Table of Contents 1 Basic results for linear equations.- Linear differential equations and linear algebraic equations.- Exponential dichotomy and L2evolutions.- 2 Hamiltonian Matrices and Algebraic Riccati equations.- Solutions of algebraic Riccati equations and graph subspaces.- Indefinite scalar products and a canonical form of Hamiltonian matrices.- Hermitian Price: $Matrix Riccati Equations in Control and Systems Theory by Hisham Abou-Kandil,available at Book Depository with free delivery worldwide.5/5(1). Find many great new & used options and get the best deals for Systems and Control Foundations and Applications: Matrix Riccati Equations in Control and Systems Theory by Vlad Ionescu, Gerhard Jank, Gerhard Freiling and Hisham Abou-Kandil (, Hardcover) at the best online prices at eBay. Free shipping for many products. An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time. A typical algebraic Riccati equation is similar to one of the following: the continuous time algebraic Riccati equation (CARE): + − − + = or the discrete time algebraic Riccati equation (DARE). Boris A. Skorohod, in Diffuse Algorithms for Neural and Neuro-Fuzzy Networks, Abstract. The recursive least squares method (RLSM) behavior on a finite interval is considered in this chapter. It is assumed that the initial value of the matrix Riccati equation is proportional to a large positive parameter otic expansions of the Riccati equation solution and the RLSM. 2 days ago Only the articles on the algebraic Riccati's equation mention equations of this form, and none of the ones about the Riccati's DE's of this form. However, this is the equation I want to find a solution to. Is there a better option than a numerical methods like Euler's or Runge-Kutta's methods. I haven't been making any progress for a while now. The main subject of this book is matrix Riccati differential equations; by definition, in this book, these are differential equations which can be written in the form $$\dot W = M_{21} (t) + M_{22} Author: Hisham Abou-Kandil, Gerhard Freiling, Vlad Ionescu, Gerhard Jank. I found this question in a differential equation textbook as a question The equation$$ \frac{dy}{dx} =A(x)y^2 + B(x)y +C(x)$\$ is called Riccati's equation show that Stack Exchange Network Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn.

A collection of functions has been implemented as a Julia package to solve several classes of Lyapunov, Sylvester and Riccati matrix equations. The goal was to demonstrate that programs written in the Julia language can achieve high computational performance, which is comparable with the performance of efficient structure exploiting Fortran.

The Riccati equation (RE), named after the Italian mathematician Jacopo Fran-cesco Riccati [10], is a basic ﬁrst-order nonlinear ordinary diﬀerential equation (ODE) that arises in diﬀerent ﬁelds of mathematics and physics [15]. It has the form y0 = P(x)+Q(x)y+R(x)y2, ()File Size: KB.

A short treatment is given of quadratic matrix equations, which are important for various applications (see, e.g., the literature cited in [4]). Conditions for solvability are listed and solutions are characterized by generalizing and improving upon certain results of Potter [6] and Kučera [5].

A splitting theorem for solutions is by: 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.

SIAM Journal on Control and OptimizationAbstract | PDF ( KB) () Computational Method for Solving a Stochastic Linear-Quadratic Control Problem Given an Unsolvable Stochastic Algebraic Riccati by: The Riccati equations () and () will be, respectively, called as the descriptor continuous-time algebraic Riccati equation (DCARE) and the descriptor discrete-time algebraic Riccati equation (DDARE).

Most of the methods, such as the Schur method, the matrix sign function method, and Newton's method, can be easily extended to solve DCARE and DDARE.The Riccati equation is one of the most interesting nonlinear differential equations of first order. It’s written in the form: where a(x), b(x), c(x) are continuous functions of x.

The Riccati equation is used in different areas of mathematics (for example, in algebraic geometry and the theory of conformal mapping), and physics.