The Stable Tracking Adaptive Fuzzy Control of Nonlinear Dynamic Systems Using the Takagi-Sugeno Fuzzy Logic

Adaptive linearization controllers have been shown to have nice performance. However, two functions in the controllers are derived from the considered system. In other words, they can only work for known systems. In this paper, the considered dynamic nonlinear model can be unknown. Next, we proposed an affined Takagi-Sugeno-type (TS-type, for short) fuzzy modeling approach to model those two unknown functions. The proposed approach is called the model reference indirect adaptive fuzzy control (MRIAFC). In this approach, a reference linear model can be used not only to characterize the desired goal for performance but also to reflect the possibility of achieving them. The Lyapunov’s stability theorem is used to derive controller parameters update laws, which ensures that the system states remain bounded and the plant output asymptotically tracks an arbitrary piecewise reference trajectory. Finally, the proposed method is successfully applied to a second-order nonlinear inverted pendulum system to verify superiority in tracking control. Keyword: Lyapunov’s stability, adaptive fuzzy control, Takagi-Sugeno.