Fixed-Time Extremum Seeking Control in the Presence of Bouc-Wen Actuator Hysteresis

Extremum Seeking Control (ESC) is a widely-used data-driven optimization algorithm employed across various domains. Despite its effectiveness, actuator nonlinearities, such as hysteresis, remain a challenge in many systems. In this paper, we introduce a novel approach leveraging high-frequency dither signals to mitigate Bouc-Wen actuator hysteresis within the existing fixed-time ESC framework. Our main result demonstrates that, with carefully selected tuning parameters, the algorithm achieves fixed-time convergence to arbitrarily small neighborhood of the optimal solution from arbitrarily large initial conditions within a predefined time interval. Simulation results validate our theoretical findings.