A Fuzzy Design for a Sliding Mode Observer-Based Control Scheme of Takagi-Sugeno Markov Jump Systems under Imperfect Premise Matching with Bio-Economic and Industrial Applications

Obaid Alshammari, Mourad Kchaou (), Houssem Jerbi, Sondess Ben Aoun and Víctor Leiva
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Obaid Alshammari: Department of Electrical Engineering, College of Engineering, University of Ha’il, Hail 2440, Saudi Arabia
Mourad Kchaou: Department of Electrical Engineering, College of Engineering, University of Ha’il, Hail 2440, Saudi Arabia
Houssem Jerbi: Department of Industrial Engineering, College of Engineering, University of Ha’il, Hail 2440, Saudi Arabia
Sondess Ben Aoun: Department of Computer Engineering, College of Computer Science and Engineering, University of Ha’il, Hail 2440, Saudi Arabia
Víctor Leiva: School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile

Mathematics, 2022, vol. 10, issue 18, 1-28

Abstract: Fuzzy theory is widely studied and applied. This article introduces an adaptive control scheme for a class of non-linear systems with Markov jump switching. The introduced scheme supposes that the system is submitted to external disturbances under imperfect premise matching. By using discrete-time Takagi–Sugeno fuzzy models, a sliding mode observer-based control scheme is utilized to estimate unmeasured states of the system. We build two fuzzy switching manifolds for the disturbance and sliding mode observer systems. Then, a linear matrix inequality-based criterion is developed using slack matrices. This criterion proves that the sliding mode dynamics are robustly admissible under an H-infinity performance often used in control theory. Hence, new adaptive sliding mode controllers are synthesized for the disturbance and sliding mode observer systems. This allows the reachability of pre-designed sliding surfaces to be guaranteed. Finally, experimental numerical illustrations on a bio-economic system and a tunnel diode circuit are presented to show potential applications, as well as validating the effectiveness of the scheme proposed in the present investigation.

Keywords: control theory; H-infinity performance; linear matrix inequalities; Markov models; premise variables; robust control; Takagi–Sugeno fuzzy models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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