<p>This paper presents a novel inverse hysteresis modeling and parameter identification approach using the grey-box neural network method for the piezo-actuated nanopositioning (PEA) stage with inherent hysteresis nonlinearity. The proposed inverse hysteresis modeling technique has been proven superior to conventional neural network modeling techniques in terms of error and learning efficiency. The grey box modeling sufficiently reduces learning time and improves model accuracy. The PEA with the proposed grey box model behaves as a linear system, allowing to implement various control algorithms to compensate its rate-dependent dynamic behavior. This study uses an integral-model predictive control (IMPC) to achieve high-frequency tracking control. The efficacy of modeling scheme with IMPC is verified experimentally and compared with black box neural network-based techniques in the literature. Results show that the proposed scheme reduces error and learning time significantly.</p>