On-line Modeling and Control via T-S Fuzzy Models for Nonaffine Nonlinear Systems Using A Second Type Adaptive Fuzzy Approach

This paper proposes a novel method for on-line modeling and robust adaptive control via Takagi–Sugeno (T-S) fuzzy models for nonaffine nonlinear systems, with external disturbances. The T-S fuzzy model is established to approximate the nonaffine nonlinear dynamic system in a linearized way. The so-called second type adaptive law is adopted, where not only the consequent part (the weighting factors) of fuzzy implications but also the antecedent part (the membership functions) of fuzzy implications are adjusted. Fuzzy B-spline membership functions (BMFs) are used for on-line tuning. Furthermore, the effect of all the unmodeled dynamics, BMF modeling errors and external disturbances on the tracking error is attenuated by a fuzzy error compensator which is also constructed from the T-S fuzzy model. In this paper, we can prove that the closed-loop system which is controlled by the proposed controller is stable and the tracking error will converge to zero. Three examples are simulated in order to confirm the effectiveness and applicability of the proposed methods in this paper.