Control Design for Interval Type-2 Fuzzy Systems Under Imperfect Premise Matching

TLDR

Imperfectly matched membership functions in interval type‑2 fuzzy‑model‑based control systems impede stability analysis. The study designs a flexible interval type‑2 fuzzy controller for nonlinear systems with parameter uncertainties, relaxing stability requirements by incorporating footprint‑of‑uncertainty information. An IT2 Takagi‑Sugeno fuzzy model with lower/upper membership functions represents the dynamics, and Lyapunov‑based linear matrix inequalities are derived to guarantee stability of the proposed controller. Simulations and experiments demonstrate the controller’s effectiveness and superiority over existing approaches.

Abstract

This paper focuses on designing interval type-2 (IT2) control for nonlinear systems subject to parameter uncertainties. To facilitate the stability analysis and control synthesis, an IT2 Takagi-Sugeno (T-S) fuzzy model is employed to represent the dynamics of nonlinear systems of which the parameter uncertainties are captured by IT2 membership functions characterized by the lower and upper membership functions. A novel IT2 fuzzy controller is proposed to perform the control process, where the membership functions and number of rules can be freely chosen and different from those of the IT2 T-S fuzzy model. Consequently, the IT2 fuzzy-model-based (FMB) control system is with imperfectly matched membership functions, which hinders the stability analysis. To relax the stability analysis for this class of IT2 FMB control systems, the information of footprint of uncertainties and the lower and upper membership functions are taken into account for the stability analysis. Based on the Lyapunov stability theory, some stability conditions in terms of linear matrix inequalities are obtained to determine the system stability and achieve the control design. Finally, simulation and experimental examples are provided to demonstrate the effectiveness and the merit of the proposed approach.