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This paper presents an extremum seeking control algorithm with an adaptivestep-size that adjusts the aggressiveness of the controller based on thequality of the gradient estimate. The adaptive step-size ensures that theintegral-action produced by the gradient descent does not destabilize theclosed-loop system. To quantify the quality of the gradient estimate, wepresent a batch least squares estimator with a novel weighting and show that itproduces bounded estimation errors, where the uncertainty is due to thecurvature of the unknown cost function. The adaptive step-size then maximizesthe decrease of the combined plant and controller Lyapunov function for theworst-case estimation error. We prove that our ESC is input-to-state stablewith respect to the dither signal. Finally, we demonstrate our proposed ESCthrough five numerical examples; one illustrative, one practical, and threebenchmarks.

Extremum Seeking Control with an Adaptive Gain Based On Gradient Estimation Error