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

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....

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 371; p. 112685
Main Authors Zhang, Liping, Fan, Hung-Yuan, Chu, Eric King-wah
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2020
Subjects
Continuous-time algebraic Riccati equation
Krylov subspace
LQR optimal control
Projection method
Projection method
15A24
Krylov subspace
93C05
LQR optimal control
65F30
Continuous-time algebraic Riccati equation
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2019.112685