We developed a new real-time control system for customizing an auditory stimulus (the binaural beat sound) by judging a user's alpha waves to entrain his/her feeling in the most relaxed way. We use an autoregressive forecasting model to estimate the frequency response series of the alpha frequency bands and a fuzzy logiccontroller to regulate the binaural beat control signal on a forecasting error signal. The arousal state determination model plays a role in regulating an appropriate binaural beat sound correlating with a change in alpha activity. According to studies of the relationship between arousal state and alpha activity, the alpha activity level may state-dependent, which can be modeled following the "inverted-U" model. The inverted-U concept is employed to determine the user arousal state, and tries to understand the user arousal state through the change in alpha activity. From the results of experiments, it is confirmed that the inverted-U model for arousal state determination is an effective model to regulate a stimulus properly with the determined arousal state.