Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations

Liping Zhang; Hung Yuan Fan; Eric King wah Chu

doi:10.1016/j.cam.2019.112685

Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations

Liping Zhang, Hung Yuan Fan, Eric King wah Chu

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

Abstract

We investigate the theory behind the Krylov subspace methods for large-scale continuous-time algebraic Riccati equations. We show that the solvability of the projected algebraic Riccati equation need not be assumed but can be inherited. This study of inheritance properties is the first of its kind. We study the stabilizability and detectability of the control system, the stability of the associated Hamiltonian matrix and perturbation in terms of residuals. Special attention is paid to the stabilizing and positive semi-definite properties of approximate solutions. Illustrative numerical examples for the inheritance properties are presented.

Original language	English
Article number	112685
Journal	Journal of Computational and Applied Mathematics
Volume	371
DOIs	https://doi.org/10.1016/j.cam.2019.112685
Publication status	Published - 2020 Jun
Externally published	Yes

Keywords

Continuous-time algebraic Riccati equation
Krylov subspace
LQR optimal control
Projection method

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.cam.2019.112685

Fingerprint Dive into the research topics of 'Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations'. Together they form a unique fingerprint.

Cite this

@article{b677142eadb148af9349078702182e63,

title = "Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations",

abstract = "We investigate the theory behind the Krylov subspace methods for large-scale continuous-time algebraic Riccati equations. We show that the solvability of the projected algebraic Riccati equation need not be assumed but can be inherited. This study of inheritance properties is the first of its kind. We study the stabilizability and detectability of the control system, the stability of the associated Hamiltonian matrix and perturbation in terms of residuals. Special attention is paid to the stabilizing and positive semi-definite properties of approximate solutions. Illustrative numerical examples for the inheritance properties are presented.",

keywords = "Continuous-time algebraic Riccati equation, Krylov subspace, LQR optimal control, Projection method",

author = "Liping Zhang and Fan, {Hung Yuan} and Chu, {Eric King wah}",

year = "2020",

month = jun,

doi = "10.1016/j.cam.2019.112685",

language = "English",

volume = "371",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier",

}

TY - JOUR

T1 - Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations

AU - Zhang, Liping

AU - Fan, Hung Yuan

AU - Chu, Eric King wah

PY - 2020/6

Y1 - 2020/6

N2 - We investigate the theory behind the Krylov subspace methods for large-scale continuous-time algebraic Riccati equations. We show that the solvability of the projected algebraic Riccati equation need not be assumed but can be inherited. This study of inheritance properties is the first of its kind. We study the stabilizability and detectability of the control system, the stability of the associated Hamiltonian matrix and perturbation in terms of residuals. Special attention is paid to the stabilizing and positive semi-definite properties of approximate solutions. Illustrative numerical examples for the inheritance properties are presented.

AB - We investigate the theory behind the Krylov subspace methods for large-scale continuous-time algebraic Riccati equations. We show that the solvability of the projected algebraic Riccati equation need not be assumed but can be inherited. This study of inheritance properties is the first of its kind. We study the stabilizability and detectability of the control system, the stability of the associated Hamiltonian matrix and perturbation in terms of residuals. Special attention is paid to the stabilizing and positive semi-definite properties of approximate solutions. Illustrative numerical examples for the inheritance properties are presented.

KW - Continuous-time algebraic Riccati equation

KW - Krylov subspace

KW - LQR optimal control

KW - Projection method

UR - http://www.scopus.com/inward/record.url?scp=85077345585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85077345585&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/24b4d43d-6962-3200-8194-b92f3bc11c16/

U2 - 10.1016/j.cam.2019.112685

DO - 10.1016/j.cam.2019.112685

M3 - Article

AN - SCOPUS:85077345585

VL - 371

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

M1 - 112685

ER -