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This paper presents a wavelet fuzzy neural network (WFNN) structure for identifying and controlling nonlinear dynamic systems. The proposed WFNN is constructed on the base of a set of fuzzy rules. Each rule includes a wavelet function in the consequent part of the rules. A training algorithm adopting a gradient descent method is employed to identify the unknown parameters in the WFNN. For the control problem, a WFNN-based predictive control (WFNNPC) law is derived via a generalized predictive performance criterion, and the control algorithm is proven to guarantee the convergence of the WFNNPC controller. The conditions of the stability analysis of the resulting control system are presented based on the Lyapunov stability theorem. Finally, the WFNN is applied in numerical simulations and experiments (identification and control of nonlinear dynamic systems and a physical positioning mechanism). The results confirm the effectiveness of the WFNN.