Stochastic time-varying extremum seeking and its applications

Abstract

We investigate a stochastic time-varying extremum seeking method based on new stochastic averaging theorems for time-varying systems and its application to distributed source seeking with switching topology. Firstly, we present sufficient conditions for the approximation of the time-varying averaging system to the time-varying original system with stochastic perturbations and obtain the solution property of the original system under the stability of invariant sets of the average system. Then, by using our developed stochastic averaging theory, we prove that the proposed stochastic time-varying extremum seeking algorithm converges to the time-varying optimal solution. Furthermore, based on the method of stochastic time-varying extremum seeking, we propose a distributed stochastic source seeking algorithm which navigates multiple vehicles to seek the source of aggregated multiple signal fields under a switching topology. We can prove the exponential convergence of such a distributed algorithm by our stochastic averaging theorems and a Lyapunov-based approach. Finally, we present detailed simulation results to illustrate the effectiveness of our method.