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Tracking control of T-S fuzzy systems under probabilistic constraints and fading channels

Author

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  • Hongjian Liu
  • Jingfei Zhang
  • Zhina Zhang

Abstract

This work investigates the probabilistic-constrained tracking control problem for T-S fuzzy systems under fading channels described by the memoryless multiplicative noise model. The main control objective is to confine the tracking error into its pre-given bounds no lower than a certain probability. To this end, a tracking controller is firstly synthesised by introducing the fading parameter as an amplification factor towards ‘retrieving’ the original information to some extent. An auxiliary function and the multi-dimensional Chebyshev inequality make it possible to derive sufficient conditions such that the tracking error falls into its specified domain with a frequency larger than a pre-given value. By employing an inequality involving unmatched membership functions of the controller and fuzzy system, the favourite property of matched membership functions can be employed. A numerical example illustrates the effectiveness of the proposed method.

Suggested Citation

  • Hongjian Liu & Jingfei Zhang & Zhina Zhang, 2025. "Tracking control of T-S fuzzy systems under probabilistic constraints and fading channels," International Journal of Systems Science, Taylor & Francis Journals, vol. 56(1), pages 88-97, January.
    • Handle: RePEc:taf:tsysxx:v:56:y:2025:i:1:p:88-97
    DOI: 10.1080/00207721.2024.2388325
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