Controlled dynamic search for a mobile object with minimum cost of light energy

We consider the optimal control problem for the spatial motion of a dynamic object in order to search for a moving object that performs simple motion in a rectangular region on a plane. As the optimality criterion, we consider a functional that takes into account the energy consumption of a light source located on the searching object. The object in question is considered to be detected when it reaches the light square with a given illumination. We propose a method for controlling the movement of a searching object, as well as the corresponding law of variation of the electric current in the light source circuit, which ensure the detection of the desired object under a guaranteed search time with minimal light energy consumption.