Heart assist devices play an important role in the treatment of heart disease. One of the key issues with these devices is the control of pump speed to satisfy multiple clinical requirements such as providing adequate cardiac output at appropriate left atrial pressure and systolic arterial pressure. A controller based on a multi-objective performance criterion is being developed at the University of Pittsburgh to fulfill these requirements. This paper describes the criterion and the penalty functions from which it is derived. The algorithm was applied to simulated cardiovascular data and to data from animals with implanted assist devices, and some preliminary results on the shape of the noninferior set defined by the penalty functions were obtained.