where the subscript t has been added to emphasize that this relationship holds for the time instant t.
The cost function consists of the weighted sum of a light quality metric, a uniformity metric for occupant comfort, and an energy consumption metric. The light quality metric penalizes the difference between the desired light field and the generated light field, while the uniformity metric enforces a penalty on the inhomogeneity of color output from adjacent light fixtures. Finally, the energy metric represents the total energy consumption of the light fixtures. Thus, the optimal lighting source intensities (u) can be obtained by solving the following optimization problem: