Residual bounds of the stochastic algebraic Riccati equation

Chun Yueh Chiang; Hung Yuan Fan

doi:10.1016/j.apnum.2012.09.007

Residual bounds of the stochastic algebraic Riccati equation

Chun Yueh Chiang
, Hung Yuan Fan^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper we consider a class of continuous-time algebraic Riccati equations with a constraint of positive definiteness, which occurs in the indefinite stochastic linear quadratic control problems and stochastic H _∞ control problems, respectively. The normwise local and non-local residual bounds are derived for a symmetric solution which approximates the unique stabilizing solution to the stochastic algebraic Riccati equation. A numerical example is presented to illustrate the sharpness of ours residual bound.

Original language	English
Pages (from-to)	78-87
Number of pages	10
Journal	Applied Numerical Mathematics
Volume	63
DOIs	https://doi.org/10.1016/j.apnum.2012.09.007
Publication status	Published - 2013 Jan

Keywords

A posteriori error bound
Forward error
Residual bound
Stabilizing solution
Stochastic algebraic Riccati equations

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.apnum.2012.09.007

Cite this

@article{32c653f65d404bcea11dca0ef07a0473,

title = "Residual bounds of the stochastic algebraic Riccati equation",

abstract = "In this paper we consider a class of continuous-time algebraic Riccati equations with a constraint of positive definiteness, which occurs in the indefinite stochastic linear quadratic control problems and stochastic H ∞ control problems, respectively. The normwise local and non-local residual bounds are derived for a symmetric solution which approximates the unique stabilizing solution to the stochastic algebraic Riccati equation. A numerical example is presented to illustrate the sharpness of ours residual bound.",

keywords = "A posteriori error bound, Forward error, Residual bound, Stabilizing solution, Stochastic algebraic Riccati equations",

author = "Chiang, \{Chun Yueh\} and Fan, \{Hung Yuan\}",

note = "Funding Information: We gratefully thank the editor and two anonymous referees for their helpful comments and suggestions that substantially improve this article. The first author would like to thank the support from National Science Council in Taiwan under grant number NSC100-2115-M-150-001.",

year = "2013",

month = jan,

doi = "10.1016/j.apnum.2012.09.007",

language = "English",

volume = "63",

pages = "78--87",

journal = "Applied Numerical Mathematics",

issn = "0168-9274",

publisher = "Elsevier BV",

}

TY - JOUR

T1 - Residual bounds of the stochastic algebraic Riccati equation

AU - Chiang, Chun Yueh

AU - Fan, Hung Yuan

N1 - Funding Information: We gratefully thank the editor and two anonymous referees for their helpful comments and suggestions that substantially improve this article. The first author would like to thank the support from National Science Council in Taiwan under grant number NSC100-2115-M-150-001.

PY - 2013/1

Y1 - 2013/1

N2 - In this paper we consider a class of continuous-time algebraic Riccati equations with a constraint of positive definiteness, which occurs in the indefinite stochastic linear quadratic control problems and stochastic H ∞ control problems, respectively. The normwise local and non-local residual bounds are derived for a symmetric solution which approximates the unique stabilizing solution to the stochastic algebraic Riccati equation. A numerical example is presented to illustrate the sharpness of ours residual bound.

AB - In this paper we consider a class of continuous-time algebraic Riccati equations with a constraint of positive definiteness, which occurs in the indefinite stochastic linear quadratic control problems and stochastic H ∞ control problems, respectively. The normwise local and non-local residual bounds are derived for a symmetric solution which approximates the unique stabilizing solution to the stochastic algebraic Riccati equation. A numerical example is presented to illustrate the sharpness of ours residual bound.

KW - A posteriori error bound

KW - Forward error

KW - Residual bound

KW - Stabilizing solution

KW - Stochastic algebraic Riccati equations

UR - https://www.scopus.com/pages/publications/84868693969

UR - https://www.scopus.com/pages/publications/84868693969#tab=citedBy

U2 - 10.1016/j.apnum.2012.09.007

DO - 10.1016/j.apnum.2012.09.007

M3 - Article

AN - SCOPUS:84868693969

SN - 0168-9274

VL - 63

SP - 78

EP - 87

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Residual bounds of the stochastic algebraic Riccati equation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this