The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation

The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation

We use a second-order learning algorithm for numerically solving a class of the algebraic Riccati equations. Specifically, the extended Hamiltonian algorithm based on manifold of positive definite symmetric matrices is provided. Furthermore, this algorithm is compared with the Euclidean gradient alg...

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Main Authors: Zhikun Luo, Huafei Sun, Xiaomin Duan
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/693659
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spelling doaj-afe6da2704a344e0a128ea775de09bb02020-11-24T23:45:58ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/693659693659The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati EquationZhikun Luo0Huafei Sun1Xiaomin Duan2School of Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaWe use a second-order learning algorithm for numerically solving a class of the algebraic Riccati equations. Specifically, the extended Hamiltonian algorithm based on manifold of positive definite symmetric matrices is provided. Furthermore, this algorithm is compared with the Euclidean gradient algorithm, the Riemannian gradient algorithm, and the new subspace iteration method. Simulation examples show that the convergence speed of the extended Hamiltonian algorithm is the fastest one among these algorithms.http://dx.doi.org/10.1155/2014/693659
collection DOAJ
language English
format Article
sources DOAJ
author Zhikun Luo
Huafei Sun
Xiaomin Duan
spellingShingle Zhikun Luo
Huafei Sun
Xiaomin Duan
The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation
Journal of Applied Mathematics
author_facet Zhikun Luo
Huafei Sun
Xiaomin Duan
author_sort Zhikun Luo
title The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation
title_short The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation
title_full The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation
title_fullStr The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation
title_full_unstemmed The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation
title_sort extended hamiltonian algorithm for the solution of the algebraic riccati equation
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description We use a second-order learning algorithm for numerically solving a class of the algebraic Riccati equations. Specifically, the extended Hamiltonian algorithm based on manifold of positive definite symmetric matrices is provided. Furthermore, this algorithm is compared with the Euclidean gradient algorithm, the Riemannian gradient algorithm, and the new subspace iteration method. Simulation examples show that the convergence speed of the extended Hamiltonian algorithm is the fastest one among these algorithms.
url http://dx.doi.org/10.1155/2014/693659
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AT xiaominduan theextendedhamiltonianalgorithmforthesolutionofthealgebraicriccatiequation
AT zhikunluo extendedhamiltonianalgorithmforthesolutionofthealgebraicriccatiequation
AT huafeisun extendedhamiltonianalgorithmforthesolutionofthealgebraicriccatiequation
AT xiaominduan extendedhamiltonianalgorithmforthesolutionofthealgebraicriccatiequation
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