Two Simple Model-free Extremum Seeking Strategies with Convergence Acceleration through Hessian Estimation

Recently, several Newton-based extremum seeking strategies have been proposed, which provide fast convergence. In this study, we focus attention on perturbation-based proportional-integral extremum seeking (PIES) and block-oriented model recursive least squares extremum seeking (BOM-RLSES), and we discuss stability and convergence, highlighting the impact of the quality of the Hessian estimation. A bioprocess application is used to compare the performance of PI and RLS Newton-based strategies with respect to the block-oriented RLSES. The results confirm the faster convergence of the Newton-based formulations for an input range contained in the region of attraction of the extremum.