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, Víctor Leiva

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number3309
JournalMathematics
Volume10
Issue number18
DOIs
StatePublished - Sep 2022
Externally publishedYes

Keywords

  • control theory
  • H-infinity performance
  • linear matrix inequalities
  • Markov models
  • premise variables
  • robust control
  • Takagi–Sugeno fuzzy models

Fingerprint

Dive into the research topics of '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'. Together they form a unique fingerprint.

Cite this