Arrangement for automatically controlling the propulsion speed of a harvesting machine, comprising: a control device having a device for establishing an optimization problem and a cost function, and having a resolution device, wherein the device for establishing the optimization problem and the cost function contains a processor which is programmed to establish a cost function and an associated optimization problem in temporally successive steps on the basis of variables describing the respective operating state of the harvesting machine and on the basis of at least one secondary condition, and the resolution device is designed to provide temporally successive sequences of actuating variables for specifying the propulsion speed, which actuation variables solve the respective optimization problem and minimize the associated cost function, a speed setting device which is configured to obtain the sequence of actuating variables for specifying the propulsion speed from the resolution device and to convert the sequence of actuating variables for specifying the propulsion speed into a sequence of absolute speeds, a monitoring device for activating an actuator influencing the propulsion speed of the harvesting machine, said monitoring device being configured to obtain from the speed setting device in each case the temporally first actuating command of each sequence of absolute speeds for specifying the propulsion speed, wherein the device for establishing the optimization problem and the cost function is connected to a device (92, 94) for determining, depending on the position of the harvesting machine, the anticipated rate of crop picked up by the harvesting machine, wherein a conversion device is programmed to calculate a sequence of anticipated positions of the harvesting machine and, on the basis of the sequence of the calculated positions and the position-dependent rates provided by the device (92, 94) for determining the anticipated rate of crop picked up by the harvesting machine, to calculate a prediction of the rate of picked-up crop and to supply said prediction as an input variable of the optimization problem to the device for establishing the optimization problem and the cost function, characterized in that the conversion device is programmed to calculate the sequence of the anticipated positions of the harvesting machine and the prediction of the rate of picked-up crop depending on time or position and to calculate the time- or position-dependent sequence of anticipated positions of the harvesting machine on the basis of the respectively present sequence of actuating commands for specifying the propulsion speed of the harvesting machine and measured and/or observed variables describing the respective operating state of the harvesting machine. a control device having a device for establishing an optimization problem and a cost function, and having a resolution device, wherein the device for establishing the optimization problem and the cost function contains a processor which is programmed to establish a cost function and an associated optimization problem in temporally successive steps on the basis of variables describing the respective operating state of the harvesting machine and on the basis of at least one secondary condition, and the resolution device is designed to provide temporally successive sequences of actuating variables for specifying the propulsion speed, which actuation variables solve the respective optimization problem and minimize the associated cost function, a speed setting device which is configured to obtain the sequence of actuating variables for specifying the propulsion speed from the resolution device and to convert the sequence of actuating variables for specifying the propulsion speed into a sequence of absolute speeds, a monitoring device for activating an actuator influencing the propulsion speed of the harvesting machine, said monitoring device being configured to obtain from the speed setting device in each case the temporally first actuating command of each sequence of absolute speeds for specifying the propulsion speed, wherein the device for establishing the optimization problem and the cost function is connected to a device (92, 94) for determining, depending on the position of the harvesting machine, the anticipated rate of crop picked up by the harvesting machine, wherein a conversion device is programmed to calculate a sequence of anticipated positions of the harvesting machine and, on the basis of the sequence of the calculated positions and the position-dependent rates provided by the device (92, 94) for determining the anticipated rate of crop picked up by the harvesting machine, to calculate a prediction of the rate of picked-up crop and to supply said prediction as an input variable of the optimization problem to the device for establishing the optimization problem and the cost function, characterized in that the conversion device is programmed to calculate the sequence of the anticipated positions of the harvesting machine and the prediction of the rate of picked-up crop depending on time or position and to calculate the time- or position-dependent sequence of anticipated positions of the harvesting machine on the basis of the respectively present sequence of actuating commands for specifying the propulsion speed of the harvesting machine and measured and/or observed variables describing the respective operating state of the harvesting machine.