The paper presents a novel technique to control the current of an electromagnetic linear actuator fed by a multilevel IGBT voltage inverter with dynamic energy storage. In order to provide short response time, high precision and low switching frequency at the same time we combine current hysteresis regulation with model predictive control (MPC). The proposed MPC technique works in very short receding horizon and includes also wavelet algorithm to optimize the MPC operation. Through simulations with real actuator data the proposed technique shows very promising results.