A General Framework for Nonlinear Model Predictive Control with Abstract Updates

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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.