Method of controlling a lithographic apparatus and device manufacturing method, control system for a lithographic apparatus and lithographic apparatus

In a method of controlling a lithographic apparatus, historical performance measurements are used to calculate a process model relating to a lithographic process. Current positions of a plurality of alignment marks provided on a current substrate are measured and used to calculate a substrate model relating to a current substrate. Additionally, historical position measurements obtained at the time of processing the prior substrates are used with the historical performance measurements to calculate a model mapping. The model mapping is applied to modify the substrate model. The lithographic apparatus is controlled using the process model and the modified substrate model together. Overlay performance is improved by avoiding over- or under-correction of correlated components of the process model and the substrate model. The model mapping may be a subspace mapping, and dimensionality of the model mapping may be reduced, before it is used.