Stochastic Control with Searching a Randomly Moving Target

The purpose of this paper is to present an optimal search algorithm for detecting a randomly moving target whose dynamics is described by the stochastic differential equation. The key notion is to formulate the problem as one of the stochastic optimal control problems and to establish the searcher´s strategy by finding the control signal minimizing the probability that the searcher fails to detect the target. First, the problem formulation is stated in connection with the search theory. Sufficient conditions for the optimal control is secondly given. Finally, a successive approximation is proposed in solving the Cauchy problem which is described by a nonlinaer integro-partial differential equation.