Stochastic Extremum Seeking for Dynamic Maps With Delays

We address a Newton-based extremum seeking algorithm for maximizing higher derivatives of unknown maps in the presence of known time delays. Different from all previous works on this topic, we employ stochastic instead of periodic perturbations, allow arbitrarily long output delays and consider a dynamic map to be optimized. We incorporate a novel predictor feedback for delay compensation and show local exponential stability along with convergence to a small neighborhood of the unknown extremum point. For the purpose of the proof, we apply a backstepping transformation and averaging theory in infinite dimensions for stochastic systems. Moreover, simulations highlight the effectiveness of the proposed predictor-feedback scheme.