Cardiac alternans are defined as the beat-to-beat oscillations of the action potential duration (APD) in paced cardiac cells and have been linked to the onset of ventricular arrythmias and even sudden cardiac death. The annihilation of these alternans is therefore a promising antiarrhythmic strategy that requires more exploration within a realm of cardiac implantable devices. In this work, a model predictive control techniques are implemented on the small amplitude of alternans parabolic partial differential equation (PDE) used to describe the alternans in a cable of cardiac cells. In our proposed control strategy, both boundary and spatially distributed actuators are applied in order to suppress the alternans along the length of the cable. We explore the optimal control strategy in which low dimensional optimal controller can successfully annihilate cardiac alternans. However, optimal controllers might violate naturally present physiological constraints and in order to address the issue of constraints present in the system, we explore the model predictive control framework that explicitly accounts for constraints. We also demonstrate an important issue of input constraints satisfaction arising from the actuator limitations (pacing limitations) and the state constraints satisfaction which are naturally present in cardiac systems in the resulting closed loop system.