Adaptive Control
Brief Stability of extremum seeking feedback for general nonlinear dynamic systems
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
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This paper presents a new approach to extremum seeking control for a class of single-input-single-output non-linear 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.