Distributed Extremum Seeking with Stochastic Perturbations

This paper considers seeking an unknown source in the two-dimensional (2D) space with a multi-agent system. Each agent has no knowledge about its own position and the distribution of the source signal. To resolve these challenges, we design distributed extrmum seeking (ES) controllers with stochastic perturbations for the multi-agent system, where each agent carries a single sensor to measure the value of the signal strength at its current position and cooperates with its neighbors. We prove the local exponential convergence of the multi-agent system, both almost surely and in probability, to a small neighborhood of the source by stochastic averaging theory. In addition, the distributed ES controllers are applied into nonholonomic unicycles by introducing a coordinate transformation. Finally, simulations illustrate the effectiveness of the distributed ES controllers.