The commonly hysteresis inverse-model based compensation approach for piezoelectric actuators is susceptible to the model uncertainties. To solve the problem, a robust pseudo-inverse control framework combining model prediction is proposed in this paper. Firstly, a NARX (nonlinear autoregressive model with exogenous inputs) model, i.e. a rate-independent dynamic hysteresis block cascading with a rate-dependent dynamic block, is employed to describe the dynamics of piezoelectric actuators. Secondly, a special hysteretic operator derived from the Prandtl–Ishlinskii (PI) model is used to extract the hysteresis changing tendency. Then the neural networks are capable of approximating the hysteresis on an expanded input space. Finally, a neural adaptive controller based on the NARX model is designed, where the neural modeling technique is strengthened to approximate and cancel out the dynamic error adaptively, avoiding the direct construction of the inversion of the hysteresis. Also, the control law and adaptive law are derived based on the Lyapunov stability analysis. Finally, the simulation results are presented to verify the effectiveness of the proposed approach.

hysteresis， adaptive control， hysteretic operator， neural networks， piezoelectric actuators