A structured doubling algorithm for discrete-time algebraic riccati equations with singular control weighting matrices

Chun Yueh Chiang, Hung Yuan Fan, Wen Wei Lin

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)933-954
Number of pages22
JournalTaiwanese Journal of Mathematics
Volume14
Issue number3 A
DOIs
Publication statusPublished - 2010 Jan 1

Fingerprint

Singular Control
Algebraic Riccati Equation
Doubling
Weighting
Discrete-time
Invertibility
Semisimple
Closed-loop
Eigenvalue
Numerical Examples

Keywords

  • Algebraic riccati equation
  • Invariant subspace
  • Singular
  • Structured doubling algorithm

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A structured doubling algorithm for discrete-time algebraic riccati equations with singular control weighting matrices. / Chiang, Chun Yueh; Fan, Hung Yuan; Lin, Wen Wei.

In: Taiwanese Journal of Mathematics, Vol. 14, No. 3 A, 01.01.2010, p. 933-954.

Research output: Contribution to journalArticle

@article{85dc4d6b74eb4b3e800d4dccb193221f,
title = "A structured doubling algorithm for discrete-time algebraic riccati equations with singular control weighting matrices",
abstract = "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.",
keywords = "Algebraic riccati equation, Invariant subspace, Singular, Structured doubling algorithm",
author = "Chiang, {Chun Yueh} and Fan, {Hung Yuan} and Lin, {Wen Wei}",
year = "2010",
month = "1",
day = "1",
doi = "10.11650/twjm/1500405875",
language = "English",
volume = "14",
pages = "933--954",
journal = "Taiwanese Journal of Mathematics",
issn = "1027-5487",
publisher = "Mathematical Society of the Rep. of China",
number = "3 A",

}

TY - JOUR

T1 - A structured doubling algorithm for discrete-time algebraic riccati equations with singular control weighting matrices

AU - Chiang, Chun Yueh

AU - Fan, Hung Yuan

AU - Lin, Wen Wei

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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.

AB - 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.

KW - Algebraic riccati equation

KW - Invariant subspace

KW - Singular

KW - Structured doubling algorithm

UR - http://www.scopus.com/inward/record.url?scp=77954160235&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954160235&partnerID=8YFLogxK

U2 - 10.11650/twjm/1500405875

DO - 10.11650/twjm/1500405875

M3 - Article

AN - SCOPUS:77954160235

VL - 14

SP - 933

EP - 954

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

SN - 1027-5487

IS - 3 A

ER -