Smart material based actuators, due to their properties of high precision, fast response, high power density, and small sizes, have become ideal actuators in many industrial applications, i.e. micro positioning, atomic force microscopy, and so forth. However, these smart actuators exhibit hysteresis nonlinear effects, which may worsen tracking performances, lead oscillations or even instabilities. Therefore, the existence of the hysteresis nonlinearities limits the utilization of smart material based actuators, and became the bottleneck of the control strategies development for systems with the smart actuators. 
 
In order to overcome the effects of the hysteresis, a number of hysteresis models have been proposed in the literatures. Among them, the Prandtl-Ishlinskii (PI) model, thanks to its significant analytical invertible property, has become one of the most popular hysteresis models. Nevertheless, the PI model can only describe a kind of symmetric, rate-independent, and non-saturated hysteresis, which restricts the use of PI model. Therefore, it requires to generalize the PI model, making it able to represent more complicated hysteresis phenomena, while keeping analytically  invertible property.
 
In this thesis, based on the PI model and the Generalized Prandtl-Ishlinskii (GPI) model available in the literature, a modified Generalized Prandtl-Ishlinskii (mGPI) model is proposed, which aims to redefine the play operator in the GPI so as to describe a kind of asymmetric and saturated hysteresis nonlinearities. 
 
According to the proposed mGPI model, an analytical inverse model is also derived, which can be used as an inverse compensator of the hysteresis nonlinearities. To validated the proposed inverse model, simulation results are provided confirming the proposed analytical inverse of the mGPI model.