Global extremum seeking by Kriging with a multi-agent system

This paper presents a method for finding the global maximum of a spatially varying field using a multi-agent system. A surrogate model of the field is determined via Kriging (Gaussian process regression) from a set of measurements collected by the agents. A criterion exploiting Kriging statistical properties is introduced for selecting new sampling points that each vehicle must rally. These new points are obtained as a compromise between improvement of the estimate of the global maximum and traveling distance. A cooperative control law is proposed to move the agents to the desired sampling points while avoiding collisions. Simulation results show the interest of the method and how it compares with a state-of-the-art solution.