A generalized structure-preserving doubling algorithm for generalized discrete-time algebraic Riccati equations

T. M. Hwang, E. K.W. Chu, W. W. Lin

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In Chu et al. (2004), an efficient structure-preserving doubling algorithm (SDA) was proposed for the solution of discrete-time algebraic Riccati equations (DAREs). In this paper, we generalize the SDA to the G-SDA, for the generalized DARE: ETXE = ATXA - (ATXB + CTS)(R + BTXB)-1(BTXA + STC) + C TQC. Using Cayley transformation twice, we transform the generalized DARE to a DARE in a standard symplectic form without any explicit inversions of (possibly ill-conditioned) R and E. The SDA can then be applied. Selected numerical examples illustrate that the G-SDA is efficient, out-performing other algorithms.

Original languageEnglish
Pages (from-to)1063-1075
Number of pages13
JournalInternational Journal of Control
Volume78
Issue number14
DOIs
Publication statusPublished - 2005 Sep 20

Fingerprint

Riccati equations

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications

Cite this

A generalized structure-preserving doubling algorithm for generalized discrete-time algebraic Riccati equations. / Hwang, T. M.; Chu, E. K.W.; Lin, W. W.

In: International Journal of Control, Vol. 78, No. 14, 20.09.2005, p. 1063-1075.

Research output: Contribution to journalArticle

@article{944adb0f7b6f4dd48800c34497aa5370,
title = "A generalized structure-preserving doubling algorithm for generalized discrete-time algebraic Riccati equations",
abstract = "In Chu et al. (2004), an efficient structure-preserving doubling algorithm (SDA) was proposed for the solution of discrete-time algebraic Riccati equations (DAREs). In this paper, we generalize the SDA to the G-SDA, for the generalized DARE: ETXE = ATXA - (ATXB + CTS)(R + BTXB)-1(BTXA + STC) + C TQC. Using Cayley transformation twice, we transform the generalized DARE to a DARE in a standard symplectic form without any explicit inversions of (possibly ill-conditioned) R and E. The SDA can then be applied. Selected numerical examples illustrate that the G-SDA is efficient, out-performing other algorithms.",
author = "Hwang, {T. M.} and Chu, {E. K.W.} and Lin, {W. W.}",
year = "2005",
month = "9",
day = "20",
doi = "10.1080/00207170500155827",
language = "English",
volume = "78",
pages = "1063--1075",
journal = "International Journal of Control",
issn = "0020-7179",
publisher = "Taylor and Francis Ltd.",
number = "14",

}

TY - JOUR

T1 - A generalized structure-preserving doubling algorithm for generalized discrete-time algebraic Riccati equations

AU - Hwang, T. M.

AU - Chu, E. K.W.

AU - Lin, W. W.

PY - 2005/9/20

Y1 - 2005/9/20

N2 - In Chu et al. (2004), an efficient structure-preserving doubling algorithm (SDA) was proposed for the solution of discrete-time algebraic Riccati equations (DAREs). In this paper, we generalize the SDA to the G-SDA, for the generalized DARE: ETXE = ATXA - (ATXB + CTS)(R + BTXB)-1(BTXA + STC) + C TQC. Using Cayley transformation twice, we transform the generalized DARE to a DARE in a standard symplectic form without any explicit inversions of (possibly ill-conditioned) R and E. The SDA can then be applied. Selected numerical examples illustrate that the G-SDA is efficient, out-performing other algorithms.

AB - In Chu et al. (2004), an efficient structure-preserving doubling algorithm (SDA) was proposed for the solution of discrete-time algebraic Riccati equations (DAREs). In this paper, we generalize the SDA to the G-SDA, for the generalized DARE: ETXE = ATXA - (ATXB + CTS)(R + BTXB)-1(BTXA + STC) + C TQC. Using Cayley transformation twice, we transform the generalized DARE to a DARE in a standard symplectic form without any explicit inversions of (possibly ill-conditioned) R and E. The SDA can then be applied. Selected numerical examples illustrate that the G-SDA is efficient, out-performing other algorithms.

UR - http://www.scopus.com/inward/record.url?scp=27844493643&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27844493643&partnerID=8YFLogxK

U2 - 10.1080/00207170500155827

DO - 10.1080/00207170500155827

M3 - Article

AN - SCOPUS:27844493643

VL - 78

SP - 1063

EP - 1075

JO - International Journal of Control

JF - International Journal of Control

SN - 0020-7179

IS - 14

ER -