Information value functions based on the Kullback-Leibler (KL) divergence have been shown the most effective for planning sensor measurements by means of greedy strategies. The problem of optimizing information value over a finite time horizon to date has been considered computationally intractable and, as proven here, is NP-hard. This paper presents new information value functions that are additive and can be optimized efficiently over time by deriving a lower bound of the KL divergence. Combined with a convex approximation of the sensor field of view, these information value functions can be used to obtain real-time sensor control by a lexicographic approach, and to derive performance guarantees. Numerical and experimental results on pedestrian data show that the lexicographic control system significantly improves target modeling and prediction performance when compared to existing algorithms.