NUMERICAL SOLUTION OF PROJECTED ALGEBRAIC RICCATI EQUATIONS

被引：12

作者：

Benner, Peter ^{[1
]}

Stykel, Tatjana ^{[2
]}

机构：

[1] Max Planck Inst Dynam Complex Tech Syst, D-39106 Magdeburg, Germany

[2] Univ Augsburg, Inst Math, D-86159 Augsburg, Germany

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2014年 / 52卷 / 02期

关键词：

projected Riccati equation; projected Lyapunov equation; Newton's method; alternating direction implicit (ADI) method; KRYLOV SUBSPACE METHODS; BALANCED TRUNCATION; LYAPUNOV EQUATIONS; MODEL-REDUCTION; POSITIVE-REAL; ALGORITHM;

D O I：

10.1137/130923993

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the numerical solution of projected algebraic Riccati equations using Newton's method. Such equations arise, for instance, in model reduction of descriptor systems based on positive real and bounded real balanced truncation. We also discuss the computation of low-rank Cholesky factors of the solutions of projected Riccati equations. Numerical examples are given that demonstrate the properties of the proposed algorithms.

引用

页码：581 / 600

页数：20

共 50 条

[41] Sensitivity of algebraic Riccati equations
Gudmundsson, T
Kenney, CS
Laub, AJ
PROCEEDINGS OF THE 35TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, 1996, : 3406 - 3411
[42] On damped algebraic Riccati equations
He, CY
Hench, JJ
Mehrmann, V
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1998, 43 (11) : 1634 - 1637
[43] Numerical Solution of Riccati Equations - Discrete Case.
Barraud, A.
Revue Francaise d'Automatique Informatique Recherche Operationnelle, 1974, 8 : 75 - 95
[44] Preserving monotonicity in the numerical solution of Riccati differential equations
Dieci, L
Eirola, T
NUMERISCHE MATHEMATIK, 1996, 74 (01) : 35 - 47
[45] Numerical computation for solving algebraic Riccati equations of weakly coupled systems
Mukaidani, Hiroaki
Xu, Hua
Monden, Yoshimi
ELECTRICAL ENGINEERING IN JAPAN, 2007, 160 (01) : 39 - 48
[46] The solution for the generalized Riccati algebraic equations of linear equality constraint system
Deng, ZC
Zhong, WX
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 1998, 19 (04) : 309 - 313
[47] LOWER BOUNDS ON THE SOLUTION OF LYAPUNOV MATRIX AND ALGEBRAIC RICCATI-EQUATIONS
KARANAM, VR
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1981, 26 (06) : 1288 - 1290
[48] HOMOTOPY METHODS FOR THE SOLUTION OF GENERAL MODIFIED ALGEBRAIC RICCATI-EQUATIONS
RICHTER, S
HODEL, AS
PRUETT, PG
IEE PROCEEDINGS-D CONTROL THEORY AND APPLICATIONS, 1993, 140 (06): : 449 - 454
[49] Upper solution bounds of the continuous and discrete coupled algebraic Riccati equations
Davies, Richard
Shi, Peng
Wiltshire, Ron
AUTOMATICA, 2008, 44 (04) : 1088 - 1096
[50] The solution for the generalized riccati algebraic equations of linear equality constraint system
Deng Zichen
Zhong Wanxie
Applied Mathematics and Mechanics, 1998, 19 (3) : 309 - 313

← 1 2 3 4 5 →