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Published on: November 24, 2021
On the stability of interval type-2 TSK fuzzy logic control systems.
Mohammad Biglarbegian1, William W Melek, Jerry M Mendel
1Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON N2L3G1, Canada. mbiglarb@uwaterloo.ca
Summary
This study introduces a new inference mechanism for interval type-2 fuzzy logic control systems, enhancing stability analysis and real-time implementation. The novel approach significantly outperforms traditional type-1 systems in control applications.
Area of Science:
- Control Systems Engineering
- Fuzzy Logic Theory
- Uncertainty Modeling
Background:
- Type-2 fuzzy logic systems excel at modeling uncertainties in control processes.
- Existing interval type-2 Takagi-Sugeno-Kang fuzzy logic control systems (IT2 TSK FLCS) require improved inference mechanisms for stability analysis.
Purpose of the Study:
- To propose a novel, closed-form inference mechanism for IT2 TSK FLCS with type-2 fuzzy antecedents and crisp consequents (A2-C0).
- To derive sufficient stability conditions and develop linear-matrix-inequality-based algorithms for IT2 TSK FLCS.
- To investigate control applications involving both plant and controller using A2-C0 TSK models, and mixed type-1/IT2 TS models.
Main Methods:
- Development of a novel closed-form inference mechanism for A2-C0 IT2 TSK FLCS.
- Derivation of stability conditions for closed-loop systems using IT2 TSK models.
- Application of linear-matrix-inequality (LMI) based algorithms for stability condition satisfaction.
- Numerical analyses and case studies comparing IT2 TSK FLCS with type-1 TSK counterparts.
Main Results:
- The proposed inference mechanism provides a closed-form solution, simplifying stability analysis.
- Sufficient stability conditions for IT2 TSK FLCS were derived and satisfied using LMI algorithms.
- Case studies demonstrated superior performance of the IT2 TSK FLCS over type-1 TSK systems.
- The novel inference engine is suitable for real-time implementation due to its simplicity.
Conclusions:
- The proposed inference mechanism enhances the stability analysis and design of IT2 TSK FLCS.
- IT2 TSK FLCS with the novel mechanism offer significant performance improvements over type-1 systems.
- The developed methods provide a foundation for advanced fuzzy logic control systems with improved uncertainty handling.
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