A hysteretic operator is proposed to set up an expanded input space so as to transform the multi-valued mapping of hysteresis to a one-to-one mapping so that the neural networks can be applied to model of the behavior of hysteresis. Based on the proposed neural modeling strategy for hysteresis, a pseudo control scheme is developed to handle the control of nonlinear dynamic systems with hysteresis. A neural estimator is constructed to predict the system residual so that it avoids constructing the inverse model of hysteresis. Thus, the control strategy can be used for the case where the output of hysteresis is unmeasurable directly. Then, the corresponding adaptive control strategy is presented. The application of the novel modeling approach to hysteresis in a piezoelectric actuator is illustrated. Then a numerical example of using the proposed control strategy for a nonlinear system with hysteresis is presented.