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Interval type-2 control design for fuzzy-model-based systems

Student thesis: Doctoral ThesisDoctor of Philosophy

Fuzzy-model-based (FMB) control framework offers a systematic and effective approach for analyzing and synthesizing nonlinear dynamic systems. This thesis focuses on control design for FMB systems under interval type-2 (IT2) fuzzy logic. Both Takagi-Sugeno (T-S) FMB systems and polynomial fuzzy-model-based (PFMB) systems are investigated. IT2 fuzzy logic has been proposed to cope with the parameter uncertainties of the nonlinear systems. The main contribution of the thesis is presented in the following three parts: In the first part, the problems of stabilization for IT2 T-S fuzzy systems with time-varying delay and parameter uncertainties are investigated. To facilitate the membership function dependent (MFD) stability analysis, piecewise linear membership functions have been employed to approximate the original upper and lower membership functions. More design exibility and practicality could be achieved by imperfect premise matching, because it is not required that the fuzzy controller and fuzzy plant have the same premise membership function and/or number of fuzzy rules. The stability conditions are derived based on Lyapunov theory and are compared with condition based on membership function independent (MFI) approach. In the second part, the problems of stabilization for IT2 T-S fuzzy systems with actuator saturation and parameter uncertainties are investigated. Following the first part, the information of the membership functions is included in the analysis. The actuator saturation is depicted and dealt with contractively invariant ellipsoid. The problem is formulated and solved with more exibility due to imperfect premise matching. In the third part, the problems of stabilization for IT2 polynomial fuzzy systems with time-varying delay and parameter uncertainties are investigated. The case has been extended from T-S FMB systems to PFMB systems compared to the first part. Because of the polynomial terms, the linear matrix inequality (LMI) approach used in the first part could not be conducted. The stability analysis is then investigated based on sum-of-squares (SOS) approach, which can be solved numerically by thirdparty toolbox. Examples are presented to show the effectiveness of the proposed approach in the thesis.
Original languageEnglish
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Award date1 Jul 2019

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