The paper presents the concept of equivalent parameter predictive control (EPPC) elaborated for semi-active fluid-based (hydraulic and pneumatic) shock absorbers equipped with controllable valves and subjected to impact excitation. The undertaken problem concerns the absorption and dissipation of the impact energy with the requirement to minimize the generated reaction force and corresponding impacting object deceleration. The development of a control strategy for a challenging problem with unknown impacting object mass and unknown changes of external and disturbance forces is proposed and discussed in detail. The innovative solution utilizes the paradigm of model predictive control supplemented by the novel concept of equivalent system parameters identification. The EPPC is based on the online measurement of system response, the computation of the equivalent mass of the impacting object, and the repetitive solution of the optimal control problem with various prediction intervals and constraints imposed on valve opening. The presented method is proven to operate robustly for unknown excitations, including double-impact conditions, and it has similar efficiency to control methods developed previously for known impact parameters.