The rate-dependent hysteresis existing in magnetostrictive actuators presents a challenge in control of these actuators. In this paper we propose a novel dynamical model for the hysteresis based on the work of Venkataraman and Krishnaprasad. The model features the coupling of the Preisach operator with an ordinary differential equation. We prove the well-posedness of the model and study identification methods for the model. An inverse control scheme is developed based on the dynamical model. The effectiveness of the identification and inverse control schemes is demonstrated through experimental results.