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

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

• calculating injection system setpoint values for actuating injection system actuators as a function of a setpoint torque by a combustion model;
• calculating gas path setpoint values for actuating gas path actuators by a gas path model;
• calculating a quality measure by an optimizer as a function of the injection system setpoint values and the gas path setpoint values, the optimizer minimizing the quality measure by changing the injection system setpoint values and gas path setpoint values within a prediction horizon;
• and setting the injection system setpoint values and the gas path setpoint values by the optimizer based on the minimized quality measure, as definitive for setting an operating point of the internal combustion engine, including minimizing the quality measure by the optimizer calculating a first quality measure at a first point in time, predicting a second quality measure within the prediction horizon at a second point in time, determining a difference between the first quality measure and the second quality measure, and setting, via the optimizer, the second quality measure as a minimized quality measure in which the deviation is smaller than a limiting value, wherein the optimizer directly predefines, as an injection system setpoint value, a rail pressure setpoint value for a subordinate rail pressure closed-loop control circuit.