State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM

Jin Zhu; Qin Ding; Maksym Spiryagin; Wanqing Xie

doi:10.1109/JAS.2016.7510217

Volume 6 Issue 3

May 2019

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2019 > 6(3): 830-837

Jin Zhu, Qin Ding, Maksym Spiryagin and Wanqing Xie, "State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM," IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 830-837, May 2019. doi: 10.1109/JAS.2016.7510217

Citation:

Jin Zhu, Qin Ding, Maksym Spiryagin and Wanqing Xie, "State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM," IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 830-837, May 2019. doi: 10.1109/JAS.2016.7510217

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State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM

doi: 10.1109/JAS.2016.7510217

1.
Department of Automation, University of Science and Technology of China, Hefei 230027, China
2.
Centre for Railway Engineering, Central Queensland University, Rockhampton 4701, Australia
3.
School of Information Science and Technology, University of Science and Technology of China, Hefei 230027, China

Funds:

the National Natural Science Foundation of China 61374073

the National Natural Science Foundation of China 61503356

Anhui Provincial Natural Science Foundation 1608085QF153

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Author Bio:
Jin Zhu (M'12) received the B.Sc. and Ph.D. degrees from the Department of Automation, University of Science and Technology of China in 2001 and 2006, respectively. From 2007−2008, he was with Hanyang University, South Korea as a post-doc and contract Professor. He joined the Department of Automation, University of Science and Technology of China in 2009. And he was a Visiting Scholar at University of Illinois at Urbana-Champaign(UIUC) from 2013−2014. His research interests include theory and application of hybrid systems. (e-mail: jinzhu@ustc.edu.cn)

Qin Ding received her M.Sc. degree from Department of Automation, University of Science and Technology of China in 2017. Her main research interest is the stability analysis of Markovian jump systems. (e-mail: dingqin@mail.ustc.edu.cn)

Maksym Spiryagin is the Deputy Director of the Centre for Railway Engineering at Central Queensland University. He received the Ph.D. degree in the field of railway transport in 2004 at the East Ukrainian National University. Professor Spiryagin's involvement in academia and railway industry projects includes research experience in Australia, China, Italy, South Korea and Ukraine involving locomotive design and traction, rail vehicle dynamics, acoustics and real-time and software-enabled control systems, mechatronics and the development of complex mechatronic systems using various approaches (co-simulation, softwarein-the-loop, processor-in-the-loop or hardware-in-the loop simulations). He has published four books and has more than 130 other scientific publications and twenty patents as one of the inventors. (e-mail: m.spiryagin@cqu.edu.au)

Wanqing Xie received the B.Sc. degree from Harbin Engineering University in 2005, the M.Sc. and Ph.D. degrees from Harbin Institute of Technology in 2008, 2012 respectively. From 2016.12-2018.12, She was a visiting scholar at Harvard University. She is currently with the School of Information Science and Technology, University of Science and Technology of China. Her research interests include stochastic systems and signal processing. (e-mail: wqxie@ustc.edu.cn)
Corresponding author: Wanqing Xie, e-mail: wqxie@ustc.edu.cn
Received Date: 2016-03-08
Revised Date: 2016-05-29
Accepted Date: 2016-06-30

Abstract

Abstract

In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems (MJLSs) with controllable mode transition probability matrix (MTPM) are investigated. In most achievements, controller design of MJLSs pays more attention to state/output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state/output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.
- Controllable mode transition probability matrix (MTPM),
- Markovian jump linear systems (MJLSs),
- stabilization,
- system cost

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References(17)

References

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State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM

doi: 10.1109/JAS.2016.7510217

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