An invariant subspace method for large-scale algebraic Riccati equation
An invariant subspace method for large-scale algebraic Riccati equation
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DOI：
10.1016/j.apnum.2009.09.006
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发表时间：
2010-11-01
影响因子：
2.8
通讯作者：
Buchot, J. -M.
中科院分区：
文献类型：
--
作者：
Amodei, L.;Buchot, J. -M.
本文通过考虑哈密顿矩阵的稳定不变子空间，给出了代数Riccati方程解的一族新的低阶逼近。它们是由ARE的解的适当表达式定义的，它推广到任意维的稳定不变子空间。保留了精确解的主要特征，特别是正半定性。对于代数Bernoulli方程，我们得到了它的精确解并给出了一种直接的计算方法。数值算例说明了该方法的有效性。(C)2009年iMac。爱思唯尔出版，版权所有。
This paper introduces a new family of low-rank approximations of the solution of the algebraic Riccati equation by considering stable invariant subspaces of the Hamiltonian matrix. They are defined from an appropriate expression of the solution of the ARE which generalizes to stable invariant subspaces of any dimension. The main features of the exact solution, in particular the positive semi-definiteness, are preserved. In the case of algebraic Bernoulli equation we obtain the exact solution and a direct method to compute it. Numerical examples illustrate the effectiveness of the proposed approach. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.