A STRUCTURED DOUBLING ALGORITHM FOR DISCRETE-TIME ALGEBRAIC RICCATI EQUATIONS WITH SINGULAR CONTROL WEIGHTING MATRICES

被引：9

作者：

Chiang, Chun-Yueh ^{[1
]}

Fan, Hung-Yuan ^{[2
]}

Lin, Wen-Wei ^{[3
]}

机构：

[1] Natl Formosa Univ, Ctr Gen Educ, Huwei 632, Taiwan

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

[3] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu 300, Taiwan

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2010年 / 14卷 / 3A期

关键词：

Algebraic Riccati equation; Invariant subspace; Structured doubling algorithm; Singular; PENCILS;

D O I：

10.11650/twjm/1500405875

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we propose a structured doubling algorithm for solving discrete-time algebraic Riccati equations without the invertibility of control weighting matrices. In addition, we prove that the convergence of the SDA algorithm is linear with ratio less than or equal 1/2 when all unimodular eigenvalues of the closed-loop matrix are semi-simple. Numerical examples are shown to illustrate the feasibility and efficiency of the proposed algorithm.

引用

页码：933 / 954

页数：22

共 13 条

[1] Solving Large-scale Discrete-time Algebraic Riccati Equations by Doubling
Lyu, Xing-Long
Li, Tiexiang
Chu, Eric King-wah
PROCEEDINGS OF THE 32ND 2020 CHINESE CONTROL AND DECISION CONFERENCE (CCDC 2020), 2020, : 4507 - 4512
[2] An efficient algorithm for the discrete-time algebraic Riccati equation
Lu, LZ
Lin, WW
Pearce, CEM
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1999, 44 (06) : 1216 - 1220
[3] The dual algebraic Riccati equations and the set of all solutions of the discrete-time Riccati equation
Zhang, Liangyin
Chen, Michael Z. Q.
Li, Chanying
INTERNATIONAL JOURNAL OF CONTROL, 2017, 90 (07) : 1371 - 1388
[4] Transformations between discrete-time and continuous-time algebraic Riccati equations
Xu, Hongguo
LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 425 (01) : 77 - 101
[5] Structured doubling algorithms for weakly stabilizing Hermitian solutions of algebraic Riccati equations
Huang, Tsung-Ming
Lin, Wen-Wei
LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (5-6) : 1452 - 1478
[6] Computational Experience with a Modified Newton Solver for Discrete-Time Algebraic Riccati Equations
Sima, Vasile
Benner, Peter
INFORMATICS IN CONTROL, AUTOMATION AND ROBOTICS (ICINCO 2018), 2020, 613 : 142 - 167
[7] STRUCTURE-PRESERVING ALGORITHMS FOR DISCRETE-TIME ALGEBRAIC MATRIX RICCATI EQUATIONS
Sima, Vasile
ICINCO 2010: PROCEEDINGS OF THE 7TH INTERNATIONAL CONFERENCE ON INFORMATICS IN CONTROL, AUTOMATION AND ROBOTICS, VOL 1, 2010, : 187 - 192
[8] On algebraic Riccati equations associated with regular singular M-matrices
Guo, Chun-Hua
Lu, Di
LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 493 : 108 - 119
[9] Numerical solution to a descriptor discrete-time algebraic Riccati equation
Oara, Cristian
Andrei, Raluca
SYSTEMS & CONTROL LETTERS, 2013, 62 (02) : 201 - 208
[10] On the discrete and continuous time infinite-dimensional algebraic Riccati equations
Staffans, OJ
SYSTEMS & CONTROL LETTERS, 1996, 29 (03) : 131 - 138

← 1 2 →