Optimal search for a Markovian target

This article is concerned with an optimal search method for detecting a randomly moving target whose dynamics are described by a stochastic differential equation. The key notions are formulating the problem as one of optimal control and establishing the searcher’s strategy by finding the control signal minimizing the probability that the searcher fails to detect the target. The search equation and the search function are derived, and sufficient conditions are given for the existence of an optimal search control. Finally, in order to circumvent difficulties arising in the realization of the optimal search algorithm, a successive approximation is presented with simulation studies.