Abstract
This paper investigates an optimal search problem under the assumption that a target to be found appears randomly and stays for a fixed time interval. We first formulate the search problem as an optimization problem to maximize the probability of finding the target while reducing the control energy consumption, and provide a solution to this problem. In this paper, we moreover derive the expectation value of how many times the target appears without being found and a necessary and sufficient condition for the agent's behavior to converge to a periodic trajectory. The effectiveness of the proposed method is demonstrated through a numerical simulation.
