Extremum Seeking Framework With Vanishing Dither Signal

The extremum-seeking (ES) control is a powerful technique for online optimization that offers theoretical guarantees for convergence to the optimizer’s neighborhood in an average sense under well-understood conditions. However, ES framework requires a time-varying dither signal to estimate the cost gradient to yield convergent results, which often result in steady-state oscillations. This paper extends the extremum-seeking control framework by replacing the fixed-amplitude dither with a dynamic system that adaptively generates a high-amplitude dither when the system is far from the optimum, and a vanishing dither as the system output approaches the local extremum. The performance of the extended ES algorithm is illustrated via numerical examples.