  Considering nonlinear processes which are subject to unknown but measurable
disturbances, we provide both stability and feasibility proofs for nonlinear
model predictive controllers with abstract updates without the use of
stabilizing terminal constraints or cost. The result utilizes a relaxed
Lyapunov inequality for the nominal system and reasonable affine Lipschitz
conditions on the open loop change of the optimal value function and the stage
costs. For this methodology, we provide proofs that the known MPC updating
techniques based on sensitivities, realtime iterations and hierachically
structured MPC updates satisfy our assumptions revealing a common stability
framework. To illustrate our approach we present a quartercar example and show
performance improvements of the updated solution with respect to comfort and
handling properties.
