This paper presents a new approach to extremum seeking control for a class of single-input-single-output nonlinear systems. With the analytic form of the performance function unknown a priori, a sliding mode observer is designed to estimate the gradient of the performance map. Based on the estimated gradient, a variable structure controller is proposed to search for the optimal operating point. We establish the conditions for the system states to enter a neighborhood of the optimal operating

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... nt, and obtain an ultimate bound on the size of the neighborhood. The robustness of the proposed controller is also discussed with respect to unmodeled fast dynamics and measurement noise.