Stability analysis of fast extremum seeking control for Wiener systems using online complex curve fitting

In this paper, we show uniform semi-global practical asymptotic stability of fast extremum seeking control (ESC) for single-input single-output Wiener systems. While classic ESC requires a time-scale separation between plant and dither, the fast ESC method circumvents this time-scale separation by exploiting limited knowledge of the frequency response of the linear part of the Wiener system, thereby achieving faster convergence. The assumptions under which the fast ESC method works are relaxed compared to existing work and explicit bounds on the design parameters of the fast ESC scheme are provided. A numerical case study illustrates the enhanced convergence and the robustness of the fast ESC method.