Method for the model-based open-loop and closed-loop of an internal combustion engine

A method for a model-based open-loop and closed-loop control of an internal combustion engine, the method comprising the steps of:

• determining, via a combustion model, a plurality of injection system setpoint values for controlling a plurality of injection system actuators, according to a setpoint torque;
• adapting, during an operation of the internal combustion engine, the combustion model according to a model value, the model value being calculated from a first Gaussian process model for representing a base grid and a second Gaussian process model for representing a plurality of adaptation data points;
• determining, by an optimizer, a minimized measure of quality by changing the plurality of injection system setpoint values within a prediction horizon, and, in an event that the minimized measure of quality is found, the plurality of injection system setpoint values are set for adjusting an operating point of the internal combustion engine;
• and
• monitoring the model value in respect of a monotony which is predefined, wherein if a monotony deviation is detected, the monotony is corrected by smoothing a plurality of data points of the second Gaussian process model to attain the monotony which is specified.