Robustly stable economic NMPC for non-dissipative stage costs

We analyze the inherent robustness properties of an economic NMPC formulation in which the controller trades off rate of convergence and economic performance. We show that this controller is input-to-state practically stable under reasonable assumptions. Our formulation does not require dissipativity with respect to the stage costs being optimized, as is required by existing economic MPC formulations. Instead, our formulation enforces dissipation in the form of a Lyapunov inequality that is constructed by using traditional tracking cost terms. Consequently, the proposed approach can be applied to a wider range of systems. We also demonstrate that the controller provides high flexibility to optimize economic performance and remains robust in the face of disturbances.