The Structure-preserving Doubling Algorithm for the Discrete Coupled Riccati Matrix Equations

Kai Wen Jiang; Zhi Li; Ying Zhang

doi:10.1109/CFASTA57821.2023.10243349

The Structure-preserving Doubling Algorithm for the Discrete Coupled Riccati Matrix Equations

Kai Wen Jiang^*
, Zhi Li
, Ying Zhang

^*Corresponding author for this work

Harbin Institute of Technology Shenzhen

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, the structure-preserving doubling algorithm (SDA) is considered to solve a discrete coupled Riccati matrix equation (DCRME) arising in Markov Jump Systems. Firstly, we transform the DCRME into a standard symplectic form using methods developed for symmetric structures. With the symplectic form, the SDA is established to obtain a positive definite solution to the DCRME. It is demonstrated that the matrix sequences generated by the SDA converge quadratically. Finally, the numerical example is provided to illustrate the effectiveness and feasibility of the presented SDA.

Original language	English
Title of host publication	Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	943-947
Number of pages	5
ISBN (Electronic)	9798350332162
DOIs	https://doi.org/10.1109/CFASTA57821.2023.10243349
State	Published - 2023
Externally published	Yes
Event	2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023 - Qingdao, China Duration: 14 Jul 2023 → 16 Jul 2023

Publication series

Name	Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023

Conference

Conference	2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023
Country/Territory	China
City	Qingdao
Period	14/07/23 → 16/07/23

Keywords

Discrete Coupled Riccati Matrix Equations
Fast convergent rate
Markov Jump Systems
Structure-preserving doubling algorithm

Access to Document

10.1109/CFASTA57821.2023.10243349

Cite this

Jiang, K. W., Li, Z., & Zhang, Y. (2023). The Structure-preserving Doubling Algorithm for the Discrete Coupled Riccati Matrix Equations. In Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023 (pp. 943-947). (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CFASTA57821.2023.10243349

Jiang, Kai Wen ; Li, Zhi ; Zhang, Ying. / The Structure-preserving Doubling Algorithm for the Discrete Coupled Riccati Matrix Equations. Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Institute of Electrical and Electronics Engineers Inc., 2023. pp. 943-947 (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023).

@inproceedings{4b66fa42430c4af7ba92a5f9189bdb6d,

title = "The Structure-preserving Doubling Algorithm for the Discrete Coupled Riccati Matrix Equations",

abstract = "In this paper, the structure-preserving doubling algorithm (SDA) is considered to solve a discrete coupled Riccati matrix equation (DCRME) arising in Markov Jump Systems. Firstly, we transform the DCRME into a standard symplectic form using methods developed for symmetric structures. With the symplectic form, the SDA is established to obtain a positive definite solution to the DCRME. It is demonstrated that the matrix sequences generated by the SDA converge quadratically. Finally, the numerical example is provided to illustrate the effectiveness and feasibility of the presented SDA.",

keywords = "Discrete Coupled Riccati Matrix Equations, Fast convergent rate, Markov Jump Systems, Structure-preserving doubling algorithm",

author = "Jiang, \{Kai Wen\} and Zhi Li and Ying Zhang",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023 ; Conference date: 14-07-2023 Through 16-07-2023",

year = "2023",

doi = "10.1109/CFASTA57821.2023.10243349",

language = "英语",

series = "Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "943--947",

booktitle = "Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023",

address = "美国",

}

Jiang, KW, Li, Z & Zhang, Y 2023, The Structure-preserving Doubling Algorithm for the Discrete Coupled Riccati Matrix Equations. in Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023, Institute of Electrical and Electronics Engineers Inc., pp. 943-947, 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023, Qingdao, China, 14/07/23. https://doi.org/10.1109/CFASTA57821.2023.10243349

The Structure-preserving Doubling Algorithm for the Discrete Coupled Riccati Matrix Equations. / Jiang, Kai Wen; Li, Zhi; Zhang, Ying.
Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 943-947 (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - The Structure-preserving Doubling Algorithm for the Discrete Coupled Riccati Matrix Equations

AU - Jiang, Kai Wen

AU - Li, Zhi

AU - Zhang, Ying

PY - 2023

Y1 - 2023

N2 - In this paper, the structure-preserving doubling algorithm (SDA) is considered to solve a discrete coupled Riccati matrix equation (DCRME) arising in Markov Jump Systems. Firstly, we transform the DCRME into a standard symplectic form using methods developed for symmetric structures. With the symplectic form, the SDA is established to obtain a positive definite solution to the DCRME. It is demonstrated that the matrix sequences generated by the SDA converge quadratically. Finally, the numerical example is provided to illustrate the effectiveness and feasibility of the presented SDA.

AB - In this paper, the structure-preserving doubling algorithm (SDA) is considered to solve a discrete coupled Riccati matrix equation (DCRME) arising in Markov Jump Systems. Firstly, we transform the DCRME into a standard symplectic form using methods developed for symmetric structures. With the symplectic form, the SDA is established to obtain a positive definite solution to the DCRME. It is demonstrated that the matrix sequences generated by the SDA converge quadratically. Finally, the numerical example is provided to illustrate the effectiveness and feasibility of the presented SDA.

KW - Discrete Coupled Riccati Matrix Equations

KW - Fast convergent rate

KW - Markov Jump Systems

KW - Structure-preserving doubling algorithm

UR - https://www.scopus.com/pages/publications/85173617438

U2 - 10.1109/CFASTA57821.2023.10243349

DO - 10.1109/CFASTA57821.2023.10243349

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AN - SCOPUS:85173617438

T3 - Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023

SP - 943

EP - 947

BT - Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023

Y2 - 14 July 2023 through 16 July 2023

ER -

Jiang KW, Li Z, Zhang Y. The Structure-preserving Doubling Algorithm for the Discrete Coupled Riccati Matrix Equations. In Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Institute of Electrical and Electronics Engineers Inc. 2023. p. 943-947. (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023). doi: 10.1109/CFASTA57821.2023.10243349

The Structure-preserving Doubling Algorithm for the Discrete Coupled Riccati Matrix Equations

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