Large-scale algebraic Riccati equations with high-rank constant terms

被引：11

作者：

Yu, Bo ^{[1
,2
]}

Fan, Hung-Yuan ^{[3
]}

Chu, Eric King-wah ^{[4
]}

机构：

[1] Hunan Univ Technol, Sch Sci, Zhuzhou 412000, Peoples R China

[2] Changsha Univ Sci & Technol, Dept Math & Stat, Changsha 410004, Hunan, Peoples R China

[3] Natl Taiwan Normal Univ, Dept Math, Taipei 116, Taiwan

[4] Monash Univ, Sch Math, 9 Rainforest Walk, Melbourne, Vic 3800, Australia

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 361卷

关键词：

Algebraic Riccati equation; Feedback gain; High-rank constant term; Large-scale problem; LQR optimal control; ITERATIVE SOLUTIONS; MATRIX EQUATIONS; PARAMETER-ESTIMATION; DOUBLING-ALGORITHM; SYSTEMS;

D O I：

10.1016/j.cam.2019.04.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the numerical solution of large-scale algebraic Riccati equations with high-rank constant terms. The solutions are not numerically low-rank, so the previously successful methods based on low-rank representations are not directly applicable. We modify the doubling algorithm, making use of the low-rank in the input matrix B. We also solve the challenging problems in the estimation of residuals and relative errors, convergence control and the output of the modified algorithm. Illustrative numerical examples are presented. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：130 / 143

页数：14

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