  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 classes of dynamic, adaptive search problems, and formulate the
resulting sensor control problems as stochastic control problems with imperfect
information, based on previous work on noisy search problems. 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
for the resulting finite-horizon stochastic control problems. We study the
problem where an individual sensor is capable of searching over multiple
sub-regions in a time, and provide a constructive algorithm for determining
optimal policies in real time based on convex optimization. We also study the
problem in which there are multiple sensors, each of which is only capable of
detecting over one sub-region in a time, jointly searching for an object.
Whereas this can be viewed as a special case of our multi-region results, we
show that the computation of optimal policies can be decoupled into
single-sensor individual scalar convex optimization problems, and provide
simple symmetry conditions where the solutions can be determined analytically.
We also consider the case where individual sensors can select the accuracy of
their sensing modes with different costs, and derive optimal strategies for
these problems in terms of the solutions of scalar convex optimization
problems. We illustrate our results with experiments using multiple sensors
searching for a single object.
