Controle Extremal Distribuído com Perturbações Estocásticas sob Atrasos

Abstract

This paper proposes the design and analysis for distributed extremum seeking control with stochastic perturbations to steer a multiagent system to an unknown source in the two-dimensional (2D) space. Each agent has no knowledge about its own position and the distribution of the source signal. To solve these challenges, we design distributed extremum seeking controllers for the multiagent system, where each agent carries a single sensor to measure partial information of the signal strength at its current position and cooperates with its neighbors. We prove the local exponential convergence of the multiagent system, both almost surely and in probability, to a small neighborhood of the source by stochastic averaging theory. In addition, the distributed extremum seeking controllers are applied into nonholonomic unicycles by introducing a coordinate transformation. Finally, a numerical example is shown to illustrate the effectiveness of the proposed predictor-based stochastic distributed extremum seeking for time-delay compensation.