A dither-free extremum-seeking control approach using 1st-order least-squares fits for gradient estimation

In this paper, we present a novel type of extremum-seeking controller, which continuously uses past data of the performance map to estimate the gradient of this performance map by means of a 1st-order least squares fit. The approach is intuitive by nature and avoids the need of dither in the extremum-seeking loop. The avoidance of dither allows for an asymptotic stability result (opposed to practical stability in dither-based schemes) and, hence, for exact convergence to the performance optimal parameter. Additionally, the absence of dither eliminates one of the time-scales of classical extremum-seeking schemes, allowing for a possibly faster convergence. A stability proof is presented for the static-map setting which relies on a Lyapunov-Razumikhin type of proof for time-delay systems. Simulations illustrate the effectiveness of the approach also for the dynamic setting.