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An adaptive backstepping terminal sliding mode control (ABTSMC) method based on a multiple−layer fuzzy neural network is proposed for a class of nonlinear systems with parameter variations and external disturbances in this study. The proposed neural network is utilized to estimate the nonlinear function to handle the unknown uncertainties of the system and reduce the switching term gain. It has a strong learning ability and high approximation accuracy due to the combination of a fuzzy neural network and recurrent neural network. The neural network parameters can be adaptively adjusted to optimal values through the adaptive laws derived from the Lyapunov theorem. To stabilize the control signal, the additional parameter adaptive law derived by the adaptive projection algorithm is used to estimate the control coefficient. The terminal sliding mode control (TSMC) is introduced on the basis of backstepping control, which can ensure that the tracking error converges in finite time. The simulation example is carried out on the DC–DC buck converter model to verify the effectiveness and superiority of the proposed control method. The contrasting results show that the ABTSMC−DHLRNN possesses higher steady−state accuracy and faster transient response.

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