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.
|Title of host publication||Proceedings of the 53rd IEEE Conference on decision and control (CDC 2014), 15-17 December 2014, Los Angeles, California|
|Place of Publication||Piscataway|
|Publisher||Institute of Electrical and Electronics Engineers|
|Number of pages||6|
|Publication status||Published - 2014|