Membership-Function-Dependent Control Design of Interval Type-2 Sampled-Data Fuzzy-Model-Based Output-Feedback Tracking Control System

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Abstract

This paper focuses on the stability analysis and control design of an interval type-2 (IT2) sampled-data (SD) fuzzy-model-based (FMB) output-feedback (OF) tracking control system which is formed by the IT2 TakagiSugeno (TS) fuzzy model, the stable reference model and the IT2SDOF fuzzy controller. The design goal is to establish a proper IT2SDOF fuzzy controller that is able to drive the states of the nonlinear plant subject to uncertainties to track those of the stable reference model, and the H performance index is adopted to optimize the tracking control performance. To improve the robustness of the IT2SDOF fuzzy controller against uncertainties of the nonlinear plant, IT2 fuzzy sets are utilized. Considering the tracking control system is SD type, a two-sided looped-functional-based approach exploiting the information on the interval from time tk to t and the interval from time t to tk+1 is applied to enhance the stability analysis. The imperfect premise matching (IPM) concept permits the number of rules and the premise membership functions of IT2 T-S fuzzy model and IT2SDOF fuzzy controller to be different which can be employed to promote the design flexibility. The tracking control system with the SD type and IPM design will cause the membership grades between IT2 T-S fuzzy model and IT2SDOF fuzzy controller to be mismatched. In addition, the membership-function-dependent (MFD) stability analysis approach that can introduce the boundary information of membership functions into the stability analysis is used to relax the stability conditions. The relaxed stability conditions subject to the H performance building on the Lyapunov stability theory are developed in terms of linear matrix inequalities (LMIs). Simulation results demonstrate the effectiveness of the proposed IT2SDFMBOF tracking control system.
Original languageEnglish
JournalIEEE Transactions on Fuzzy Systems
DOIs
Publication statusE-pub ahead of print - 24 Nov 2021

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