Robust Stability and Performance Bounds for MPC with Abstract Updates

In this paper we present a stability proof of model predictive control without stabilizing terminal constraints or cost which are subject to unknown but measurable disturbances. To this end, a relaxed Lyapunov argument on the nominal system and Lipschitz conditions on the open loop change of the optimal value function and the stage costs are employed. Based on the special case of sensitivity analysis, we show that the Lipschitz assumptions are satisfied if a sensitivity update can be performed along the closed loop solution. To illustrate our approach we present a halfcar example and show performance improvement of the updated solution with respect to comfort and handling properties.