Extremum seeking (ES) control is an online optimization algorithm that estimates the gradient of an unknown objective function to search for and maintain its optimal point. Owing to its simple controller structure and guaranteed stability, ES has been applied to a wide range of systems. However, in practical applications, the explainability of the estimated optimal solution remains a challenge. In recent years, various approaches have been proposed to accelerate convergence by estimating higher-order derivatives. This paper extends such approaches by introducing a Kalman filter to estimate the unknown objective function itself. The proposed method not only improves the explainability of ES but also has the potential to enhance convergence speed. The effectiveness of the method is demonstrated through numerical examples.
Makino et al. (Sat,) studied this question.