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 convergence of the Newton algorithm is proved to be independent of the Hessian matrix and can be arbitrarily assigned, which is an advantage over the standard gradient-based stochastic extremum seeking. Simulation shows the effectiveness and advantage of the proposed algorithm over gradient-based stochastic extremum seeking.