This paper presents a control algorithm for seismic mixed base isolation, combining passive isolators and semi-active viscous dampers. The objective is to limit base displacement while avoiding undesirable amplification of the response of the non-isolated modes. To this end, the proposed algorithm takes into account the constraints on the damping coefficient of the semi-active damper and information on the excitation. It is based on the approximate iterative solution, at each control time step, of a nonlinear inhomogeneous constrained optimal control problem. An autoregressive model is used to obtain, at each control time step, a prediction of the upcoming excitation in a short time interval ahead. Numerical simulation results demonstrate the efficacy of the above method, especially in improving floor response spectra, and its superiority with respect to clipped-optimal algorithms.