This paper presents a new training method for fuzzy neural network (FNN) systems to approximate unknown nonlinear continuous functions. Fast terminal sliding mode combining the 3nite time convergent property of terminal attractor and exponential convergent property oflinear system has faster convergence to the origin in 3nite time. The proposed training algorithm uses the principle ofthe fast terminal sliding mode into the conventional gradient descent learning algorithm. The Lyapunov stability analysis in this paper guarantees that the approximation is stable and converges to the optimal approximation function with improved speed instead of3nite time convergence to unknown function. The proposed FNN approximator is then applied in the control ofan unstable nonlinear system and the Du5ng system. The simulation results demonstrate the effectiveness of the proposed method
