Conference Proceedings

A Unifying Approach to Extremum Seeking: Adaptive Schemes Based on Estimation of Derivatives

D Nesic, Y Tan, WH Moase, C Manzie

49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC) | IEEE | Published : 2010

Abstract

A unifying, prescriptive framework is presented for the design of a family of adaptive extremum seeking controllers. It is shown how extremum seeking can be achieved by combining an arbitrary continuous optimization method (such as gradient descent or continuous Newton) with an estimator for the derivatives of the unknown steady-state reference-to-output map. A tuning strategy is presented for the controller parameters that ensures non-local convergence of all trajectories to the vicinity of the extremum. It is shown that this tuning strategy leads to multiple time scales in the closed-loop dynamics, and that the slowest time scale dynamics approximate the chosen continuous optimization meth..

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