This article proposes an adaptive predictive control design technique to mitigate the displacement in a hysteretical base-isolated system seismically perturbed. The obtained predictive control law is based on the measurable linear part of the base-isolated model, and programmed over a prediction-time of one-sampling-discrete-time period. Two main contributions are highlighted. First, we use a delta-modulator with hysteresis to avoid the zero-crossing in the control law caused by one estimated parameters. Second, we implement a dynamic hysteretic model based on relays as a command governor able to create new hysteretic reference trajectories. This is realized to robustly compensate the hysteretic behavior of the structure under control. Finally, and according to numerical experiments, our control design presents a good performance from the displacement control point of view in comparison to the open-loop system response, where the El Centro earthquake is invoked.