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
N1 - Funding Information:
Part of the work occurred when the first and third authors visited the School of Mathematical Sciences at Fudan University. The first and the second authors were supported by the National Natural Science Foundation, China (Grant 11601484 ) and the Ministry of Science and Technology, Taiwan (Grant #MOST-108-2115-M-003-004) , respectively. Appendix
Funding Information:
Part of the work occurred when the first and third authors visited the School of Mathematical Sciences at Fudan University. The first and the second authors were supported by the National Natural Science Foundation, China (Grant 11601484) and the Ministry of Science and Technology, Taiwan (Grant #MOST-108-2115-M-003-004), respectively.
Publisher Copyright:
© 2019 Elsevier B.V.
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
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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 -