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The theoretical and experimental studies of a reinforcement discrete neuro-adaptive control for unknown piezoelectric actuator systems with dominant hysteresis are presented. Two separate nonlinear gains, together with an unknown linear dynamical system, construct the nonlinear model (NM) of the piezoelectric actuator systems. A nonlinear inverse control (NIC) according to the learned NM is then designed to compensate the hysteretic phenomenon and to track the reference input without the risk of discontinuous response. Because the uncertainties are dynamic, a recurrent neural network (RNN) with residue compensation is employed to model them in a compact subset. Then, a discrete neuro-adaptive sliding-mode control (DNASMC) is designed to enhance the system performance. The stability of the overall system is verified by Lyapunov stability theory. Comparative experiments for various control schemes are also given to confirm the validity of the proposed control.