Gradient-Based Extremum Seeking: Performance Tuning via Lie Bracket Approximations

In this paper, we propose model-free extremum seeking systems approximating a filtered-gradient descent law, instead of a simple gradient descent law. Namely, we consider that the gradient is low pass filtered before being fed in the gradient descent law. Exploiting the Lie bracket formalism, we derive general classes of systems that approximate the filtered- gradient descent law, and we focus on four particular schemes. The first ensures the boundedness of the update rates. The last three adapt the dither amplitude to enhance the steady state accuracy. The performances of those schemes are analyzed in simulation and compared with the performances of extremum seeking systems approximating a simple gradient descent law.