Iterative algorithms for discrete periodic Riccati matrix equations

Abstract

In this paper, two iterative algorithms are constructed to obtain the positive definite solutions of the discrete periodic algebraic Riccati matrix equations. In these two algorithms, the estimation of the unknown matrices are updated by using the available estimation information at the current iteration step. The convergence properties of the proposed algorithms are also given. Finally, numerical examples are employed to illustrate the effectiveness of the proposed algorithms.

Keywords:

• Periodic Riccati equations
• monotonicity
• boundedness
• convergence

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Shenzhen Municipal Project for International Cooperation with Project No. GJHZ20180420180849805, by Shenzhen Municipal Basic Research Project for Discipline Layout with Project No. JCYJ20170811160715620, by the Fundamental Research Funds for the Central Universities [grant number HIT.BRETIV.201907], by National Natural Science Foundation of China for Excellent Young Scholars [grant number 61822305], by Guangdong Natural Science Foundation under Grant No. 2017A030313340, and Shenzhen Municipal Basic Research Project for Discipline Layout with Project No. JCYJ20180507183437860.

Notes on contributors

Ai-Guo Wu

Ai-Guo Wu was born in Gong’an County, Hubei Province, P. R. China on September 20, 1980. He received his B. Eng. degree in Automation in July 2002, M. Eng. degree in Navigation, Guidance and Control in July 2004, and Ph.D. degree in Control Science and Engineering in November 2008 all from Harbin Institute of Technology. In October 2008, he joined Harbin Institute of Technology Shenzhen Graduate School, where he is now a professor. Prof. Wu visited City University of Hong Kong from March 2009 to March 2011 as a Research Fellow. His research interests include descriptor systems, conjugate product of polynomials, switched systems. Prof. Wu is a Reviewer for American Mathematical Review. He was an Outstanding Reviewer for IEEE Transactions on Automatic Control. He received the National Natural Science Award (Second Prize) in 2015 from P. R. China, and the National Excellent Doctoral Dissertation Award in 2011 from the Academic Degrees Committee of the State Council and the Ministry of Education of P. R. China. He was supported by the Program for New Century Excellent Talents in University in 2011.

Ying Zhang

Ying Zhang was born in Jilin Province, P. R. China. She received her M. Eng. degree in Control Theory and Control Engineering from Harbin University of Science and Technology in 2003, and Ph.D. degree in Control Science and Engineering in 2007 from Harbin Institute of Technology. From 2007 to 2010, she was a postdoctoral researcher in Harbin Institute of Technology Shenzhen Graduate School, where she became an assistant professor in 2010, and an associate professor in 2011. Her main research interests include robust control and filter theory, iteration based control methods.

Tong-Yang Jiang

Tong-Yang Jiang was born in Qitaihe City, Heilongjiang Province , P.R.China on June 16, 1993. He received his B. Eng. degree in Automation in July 2014 from Harbin Institute of Technology, M. Eng. degree in Control Engineering in January 2017 from Harbin Institute of Technology Shenzhen Graduate School. In May 2017, he joined Beijing Aerospace Automatic Control Institute, where he is now an engineer. His research interests include control theory and control system simulation.