Variable structure extremum seeking control based on sliding mode gradient estimation for a class of nonlinear systems

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 point, 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.