Abstract
In this paper, we derive the design and analysis for scalar gradient extremum seeking (ES) subject to arbitrarily long input–output delays, by employing a predictor with a perturbation-based estimate of the Hessian. Exponential stability and convergence to a small neighborhood of the unknown extremum point can be guaranteed. This result is carried out using backstepping transformation and averaging in infinite dimensions. Generalization of the results for Newton-based ES is also indicated. Some simulation examples are presented to illustrate the performance of the delay-compensated ES control scheme.
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