Optimal search plan minimizing the expected risk of the search for a target with conditionally deterministic motion

This article deals with a search problem for a moving target with a rather simple type of motion called factorable conditionally deterministic. A search plan is characterized by (ϕ, T), the elements of which specify how to search and when to stop the search, respectively. The problem is to find the optimal search plan which minimizes the expected risk (the expected search cost minus the expected reward). We obtain conditions for the optimal search plan, and applying the theorems, we derive the optimal search plan in a closed form for the case in which the target moves straight from a fixed point selecting his course and speed randomly.