TY - JOUR
T1 - Large-scale algebraic Riccati equations with high-rank constant terms
AU - Yu, Bo
AU - Fan, Hung Yuan
AU - Chu, Eric King wah
N1 - Funding Information:
Part of the work occurred when the first author visited Monash University and the third author visited the School of Mathematical Sciences at Fudan University. The first author was supported partly by the NSF of China (grant 11301170, 11801163), Natural Science Foundation of Hunan Province (2017JJ2071) and the Excellent Youth Foundation and General Foundation of Hunan Educational Department (17B071, 17C0466). The second author was supported partly by the Ministry of Science and Technology in the Taiwan, ROC (Grant No: MOST 107-2115-M-003-003).
Funding Information:
Part of the work occurred when the first author visited Monash University and the third author visited the School of Mathematical Sciences at Fudan University. The first author was supported partly by the NSF of China (grant 11301170 , 11801163 ), Natural Science Foundation of Hunan Province ( 2017JJ2071 ) and the Excellent Youth Foundation and General Foundation of Hunan Educational Department ( 17B071 , 17C0466 ). The second author was supported partly by the Ministry of Science and Technology in the Taiwan, ROC (Grant No: MOST 107-2115-M-003-003 ).
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - We consider the numerical solution of large-scale algebraic Riccati equations with high-rank constant terms. The solutions are not numerically low-rank, so the previously successful methods based on low-rank representations are not directly applicable. We modify the doubling algorithm, making use of the low-rank in the input matrix B. We also solve the challenging problems in the estimation of residuals and relative errors, convergence control and the output of the modified algorithm. Illustrative numerical examples are presented.
AB - We consider the numerical solution of large-scale algebraic Riccati equations with high-rank constant terms. The solutions are not numerically low-rank, so the previously successful methods based on low-rank representations are not directly applicable. We modify the doubling algorithm, making use of the low-rank in the input matrix B. We also solve the challenging problems in the estimation of residuals and relative errors, convergence control and the output of the modified algorithm. Illustrative numerical examples are presented.
KW - Algebraic Riccati equation
KW - Feedback gain
KW - High-rank constant term
KW - Large-scale problem
KW - LQR optimal control
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U2 - 10.1016/j.cam.2019.04.014
DO - 10.1016/j.cam.2019.04.014
M3 - Article
AN - SCOPUS:85065056688
SN - 0377-0427
VL - 361
SP - 130
EP - 143
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -