The problem of searching for an unknown object occurs in important applications ranging from security, medicine and defense. Sensors with the capability to process information rapidly require adaptive algorithms to control their search in response to noisy observations. In this paper, we discuss a class of dynamic, adaptive search problems, and formulate the resulting sensor control problems as stochastic control problems with imperfect information. The structure of these problems, with objective functions related to information entropy, allows for a complete characterization of the optimal strategies and the optimal cost. We study problems that involve both individual sensors as well as multiple sensors. We provide a constructive algorithm for determining optimal policies in real time based on convex optimization. We also show that, under symmetry conditions on the observation errors in the sensors, the optimal policies have a simple characterization that lead to a closed-form solution for the convex optimization problem. We illustrate the results with simulations including two sensors searching for a single object.