Observer-Based SMC for Discrete Interval Type-2 Fuzzy Semi-Markov Jump Models

This study is devoted to the observer-based sliding mode control (SMC) for discrete nonlinear semi-Markov jump models with incomplete sojourn information and application to the quarter-car suspension model. The nonlinear plant with parameter uncertainty is represented by an interval type-2 fuzzy mod...

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Bibliographic Details
Published inIEEE transactions on fuzzy systems Vol. 33; no. 6; pp. 1913 - 1925
Main Authors Qi, Wenhai, Li, Runkun, Shi, Peng, Zong, Guangdeng
Format Journal Article
LanguageEnglish
Published IEEE 01.06.2025
Subjects
Biological system modeling
Computational modeling
Fuzzy systems
Internal type-2 fuzzy (IT2F) model
Probability density function
probability density functions
Sliding mode control
sliding mode control (SMC)
Stability criteria
Switches
Technological innovation
Training
Uncertainty
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Summary:This study is devoted to the observer-based sliding mode control (SMC) for discrete nonlinear semi-Markov jump models with incomplete sojourn information and application to the quarter-car suspension model. The nonlinear plant with parameter uncertainty is represented by an interval type-2 fuzzy model, where the membership functions of the fuzzy rules are related to the system mode. Since sojourn information is challenging to obtain in practice, the sojourn time probability density function is considered to be incompletely available. The considered system is more general, not only relaxing the traditional assumption that all the sojourn time probability density functions are completely available, but also covering completely available sojourn time probability density functions as a special case. The main innovation is that an observer-based SMC scheme is designed, which makes the discrete nonlinear models have better dynamic performance, and realizes the reachability of discrete quasi-sliding mode. By the interval type-2 fuzzy and classical Lyapunov function, the mean-square stability criterion of the semi-Markov jump models is constructed employing additional matrix variables. Then, an observer-based SMC mechanism is constructed to achieve the reachability of the quasi-sliding mode. Ultimately, the proposed method is validated by a two-degree-freedom quarter-car suspension model.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2025.3545895