Lie bracket approximation-based extremum seeking with vanishing input oscillations

Learning generalized Nash equilibria in monotone games: A hybrid adaptive extremum seeking control approach

“…The secondary goal cannot be accomplished by techniques that diminish the oscillation amplitude over time (Abdelgalil & Taha, 2021;Bhattacharjee & Subbarao, 2021) as the cost functions are slowly-varying and the learning procedure would stop prematurely. Furthermore, we cannot use too high frequencies (Suttner, 2019) as that would also destroy our equipment.…”

Recursive Averaging with Application to Bio-Inspired 3D Source Seeking

“…Then, the stability properties of the averaged system are transferred to the practical stability for the original system. In a recent effort, the approach was utilized in analyzing extremum seeking systems with the introduction of the Lie Bracket Approximation framework [16], [17], [18], [19].…”

A Graphical Approach to Examining Classical Extremum Seeking Using Bifurcation Analysis

“…Manuscript received March 22, 2022 recently, the Lie bracket averaging method [14][15][16] can retain the harmonic-forcing dynamics, but this approach remains mathematically rigorous. On the computational front, recent works have successfully employed numerical continuation using the AUTO-07P software to analyse extremum seeking controllers [17][18][19][20].…”