Stochastic Averaging for Time-Varying Systems and Its Applications to Distributed Stochastic Source Seeking

Abstract

We investigate stochastic averaging theory for time-varying nonlinear systems and its applications to convergence analysis of a distributed source seeking algorithm with time-varying topology. First, we present continuous-time stochastic averaging theorems for time-varying nonlinear systems with stochastic perturbations. Based on the method of stochastic extremum seeking, we propose a distributed stochastic source seeking algorithm with switching topology. We navigate multiple vehicles to seek the source of an unknown signal field, using the measurements of the signal field at their own positions and relative positions to their neighbors. Then, we apply our extended stochastic averaging theory to prove the local exponential convergence, both almost surely and in probability, to a small neighborhood near the source. Finally, a numerical example is included to illustrate the effectiveness of the algorithm.