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In recent years, an approach to extremum seeking control made it possible todesign control vector fields that lead to asymptotic stability of the minimumpoint provided that the minimum value of the function is known a priori. Inthis work, we aim to relax that assumption. We propose an extremum-seekingcontrol law that converges to the minimum point with vanishing controloscillations, without access to the minimum value of the cost function. Weprovide a numerical example to support our results.

Lie Bracket Approximation-Based Extremum Seeking with Vanishing Input Oscillations