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

Authors:
Lina Fu;ímit Özgüner
Affiliations:
Xerox Corporation, Webster, NY, 14580, USA;Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

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.