Retrospective Cost-Based Extremum Seeking Control with Vanishing Perturbation for Online Output Minimization

Extremum-seeking control (ESC) is a powerful technique for online optimization that offers theoretical guar-antees for convergence to the optimizer's neighborhood under well-understood conditions. However, ESC requires a nonconstant perturbation signal to provide persistent excitation to the target system to yield convergent results, which usually results in steady state oscillations. While certain techniques have been proposed to eliminate perturbations once the neighborhood of the minimizer is reached, system modifications and environmental perturbations can suddenly change the minimizer, and nonconstant perturbations would once more be required to converge to the new minimizer. Hence, this paper develops a retrospective cost-based ESC (RC/ESC) technique for online output minimization with a vanishing perturbation, that is, a perturbation that becomes zero as time increases independently from the state of the controller or the controlled system. The performance of the proposed algorithm is illustrated via numerical examples.