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In this paper, an adaptive cerebellar-model articulation computer (CMAC) neural network (NN) control system is developed for a linear piezoelectric ceramic motor (LPCM) that is driven by an LLCC-resonant inverter. The motor structure and LLCC-resonant driving circuit of an LPCM are introduced initially. The LLCC-resonant driving circuit is designed to operate at an optimal switching frequency such that the output voltage will not be influenced by the variation of quality factor. Since the dynamic characteristics and motor parameters of the LPCM are highly nonlinear and time varying, an adaptive CMAC NN control system is designed without mathematical dynamic model to control the position of the moving table of the LPCM drive system to achieve high-precision position control with robustness. In the proposed control scheme, the dynamic backpropagation algorithm is adopted to train the CMAC NN online. Moreover, to guarantee the convergence of output tracking error for periodic commands tracking, analytical methods based on a discrete-type Lyapunov function are utilized to determine the optimal learning-rate parameters of the CMAC NN. The effectiveness of the proposed driving circuit and control system is verified by experimental results in the presence of uncertainties, and the advantages of the proposed control system are indicated in comparison with a traditional integral-proportional position control system. Accurate tracking response and superior dynamic performance can be obtained due to the powerful online learning capability of the CMAC NN with optimal learning-rate parameters.