A system for mimicking daylight in a space by using one or more light sources (11,12) having a redirectable light output is configured to determine a daylight-mimicking light output direction (51,52) for the light output in the space based on a time of day, determine an estimated or detected position of an object, person (59) or animal in the space, determine an adjusted light output direction (51,53) for the one or more light sources in dependence on the daylight-mimicking light output direction and the estimated or detected position, and control the one or more light sources to render the light output in the adjusted light output direction.