Fuzzy Control and Filtering for Nonlinear Singularly Perturbed Markov Jump Systems

Yueying Wang, Choon Ki Ahn, Huaicheng Yan, Shaorong Xie

Research output: Contribution to journalArticlepeer-review

100 Citations (Scopus)

Abstract

This article addresses the control and filtering problems for Markov jump singularly perturbed systems approximated by Takagi-Sugeno fuzzy models. The underlying transition probabilities (TPs) are assumed to vary randomly in a finite set, which is characterized by a higher level TP matrix. The mode-and variation-dependent fuzzy static output-feedback controller (SOFC) and filter are designed, respectively, to fulfill the control and filtering purposes. To facilitate the fuzzy SOFC synthesis, the closed-loop system is transformed into a fuzzy piecewise-homogeneous Markov jump singularly perturbed descriptor system (MJSPDS) by descriptor representation. A rigorous proof of mean-square exponential admissibility for the resulting fuzzy MJSPDS is presented. The criterion ensuring the mean-square exponential stability of the fuzzy filtering error system is further formed based on similar procedures. By setting the specific forms of the related matrix variables, the solutions for the predesigned fuzzy SOFC and filter are furnished, respectively. Finally, feasibility and validities of the developed fuzzy control and filtering results are verified by two practical examples.

Original languageEnglish
Article number9146349
Pages (from-to)297-308
Number of pages12
JournalIEEE Transactions on Cybernetics
Volume51
Issue number1
DOIs
Publication statusPublished - 2021 Jan

Bibliographical note

Funding Information:
Manuscript received October 22, 2019; revised April 5, 2020; accepted June 14, 2020. Date of publication July 22, 2020; date of current version December 22, 2020. This work was supported in part by the National Natural Science Foundation of China under Grant 61973204, Grant 61703275, and Grant 61673178; in part by the Shanghai and HongKong-Macao-Taiwan Science and Technology Cooperation Project under Grant 19510760200; and in part by the China Postdoctoral Science Foundation under Grant 2019M660117. This article was recommended by Associate Editor J. Qiu. (Corresponding authors: Yueying Wang; Huaicheng Yan.) Yueying Wang and Shaorong Xie are with the School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China (e-mail: wyy676@126.com; srxie@shu.edu.cn).

Publisher Copyright:
© 2013 IEEE.

Keywords

  • Filtering
  • Takagi-Sugeno fuzzy model
  • output-feedback control
  • piecewise-homogeneous Markov jump system
  • singularly perturbed system (SPS)

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Information Systems
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering

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