Regenerative suspensions are becoming a potential to achieve active suspensions without reducing fuel economy. In this paper, a model predictive controller (MPC) is developed to minimize sprung mass vertical acceleration or maximize the energy regenerated by the suspension. MPC has difficulties when harvested energy is the optimization function. This led to development of an MPC algorithm that includes Lyapunov constraints that stabilizes the system states. Simulation results show that optimizing the energy output of the system increases energy production but degrades the ride comfort. Implementation of the Lyapunov constraints help reduce ride degradation and increase ride while improving energy regeneration.