Towards a sampled-data theory for nonlinear model predictive control

This paper considers the stability, robustness and output feedback problem for sampled-data nonlinear model predictive control (NMPC). Sampled-data NMPC here refers to the repeated application of input trajectories that are obtained from the solution of an open-loop optimal control problem at discrete sampling instants. Specifically we show that, under the assumption that the value function is continuous, sampled-data NMPC possesses some inherent robustness properties. The derived robustness results have a series of direct implications. For example, they underpin the intuition that small errors in the optimal input trajectory, e.g. resulting from an approximate numerical solution, can be tolerated. Furthermore, the robustness can be utilized to design observer-based semi-globally stable output feedback NMPC schemes.