Information-driven control can be used to develop intelligent sensors that can optimize their measurement value based on environmental feedback. In object tracking applications, sensor actions are chosen based on the expected reduction in uncertainty also known as information gain. Random finite set (RFS) theory provides a formalism for quantifying and estimating information gain in multi-object tracking problems. However, estimating information gain in these applications remains computationally challenging. This paper presents a new tractable approximation of the RFS expected information gain applicable to sensor control for multi-object search and tracking. Unlike existing RFS approaches, the information gain approximation presented in this paper considers the contributions of non-ideal noisy measurements, missed detections, false alarms, and object appearance/disappearance. The effectiveness of the information-driven sensor control is demonstrated through two multi-vehicle search-while-tracking experiments using real video data from remote terrestrial and satellite sensors.