There is described a method for controlling a system, for example a Diesel engine, that is subject to transient changes of target outputs. The target outputs specify outputs required from the system. "Steady state" information is used to give optimum inputs for the system when the target outputs are substantially constant. A model of the system is used to predict the outputs of the system in response to candidate new values for the inputs of the system. The method combines the steady state information with the predicted response of the system to determine inputs to the system which will cause the system outputs to match the target outputs as closely as possible. For each candidate (in one embodiment), the method calculates the difference between the steady state inputs and a candidate, and the difference between the target outputs and the predicted outputs that would result from the adoption of that candidate, to determine an optimum candidate which is then used to update the inputs to the system.