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In this paper, an adaptive generalized predictive control method using adaptive-network-based fuzzy-inference system (ANFIS) and multiple models is proposed for a class of uncertain discrete-time nonlinear systems with unstable zero-dynamics. The proposed controller consists of a linear and robust generalized predictive adaptive controller, a nonlinear generalized predictive adaptive controller based on ANFIS, and a switching mechanism. It has been shown that the linear generalized predictive adaptive controller can ensure the boundedness of the input and output signals, and the nonlinear generalized predictive controller can improve the transient performance of the system. By switching between the two earlier described controllers, the switching mechanism can simultaneously improve the performance and ensure the closed-loop stability. Moreover, the method has relaxed the global boundedness assumption of the higher order nonlinear term and established the analysis of stability and convergence of the closed-loop system. In the proposed controller, ANFIS is adopted to estimate and compensate the unmodeled dynamics, which avoids some possible flaws of a backpropagation (BP) neural network. Simulation results have demonstrated the superiority of the proposed method and verified the theoretical analysis.