Extremum seeking with sliding mode gradient estimation and asymptotic regulation for a class of nonlinear systems

This paper presents a model-based extremum seeking approach for a class of single-input single-output nonlinear systems, with the analytic form of the performance function unknown a priori. We focus on a practically implementable design with robustness to model uncertainties and disturbances. A discrete-time sliding mode gradient estimator is developed for estimating the gradient of the performance profile. Based on the estimate, a variable structure output feedback regulator is proposed to enforce the system states toward the optimal trajectory. We analyze convergence conditions of the switching system toward a neighborhood of the optimal trajectory, and establish an ultimate bound on the size of the neighborhood. The robustness of the proposed controller is discussed with respect to measurement noise. (C) 2011 Elsevier Ltd. All rights reserved.