Extremum Seeking Without Transient Misdirection: An Adaptive Observer-Based Approach

This paper deals with transient misdirection in an observer-based extremum seeking (ES) scheme, during which the ES system starts operating with an erroneous sign in the gradient estimation. Based on a preliminary analysis of how mild this misdirection could be with aggressively tuned parameters, we introduce an adaptive observer whose gain varies with the observer error: a high gain during transients and a low gain during steady states, and provide a semi-global stability result of the proposed approach. Simulation examples performed on both a static plant and a Hammerstein plant show the advantage that the proposed approach can eliminate transient misdirection while maintaining satisfactory performance.