Newton-based stochastic extremum seeking

In this paper, we introduce a Newton-based approach to stochastic extremum seeking and prove local stability of Newton-based stochastic extremum seeking algorithm in the sense of both almost sure convergence and convergence in probability. The advantage of the Newton approach is that, while the convergence of the gradient algorithm is dictated by the second derivative (Hessian matrix) of the map, which is unknown, rendering the convergence rate unknown to the user, the convergence of the Newton algorithm is proved to be independent of the Hessian matrix and can be arbitrarily assigned. Simulation shows the effectiveness and advantage of the proposed algorithm over gradient-based stochastic extremum seeking.