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

Abstract

In this paper, we present a novel type of extremumseeking 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 extremumseeking 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. 53rd IEEE Conference on Decision and Control

Asymptotic Stability of Perturbation-Based Extremum-Seeking Control for Nonlinear Plants

“…, n u , where η ω ∈ R >0 is a time-varying tuning parameter. We note that if η ω is constant, the perturbation signals in (12) are given by ω 1 = sin(η ω t), ω 2 = cos(η ω t), ω 3 = sin(2η ω t), etcetera. The use of sinusoidal perturbations with constant angular frequencies is common in extremumseeking control; see for example [1], [29] and references therein.…”

“…In addition, a few references describe asymptotic behavior for extremum-seeking methods that do not rely on added perturbations; see for example [10], [12]. It is shown in [12] that asymptotic convergence to the optimal plant performance can be obtained with an extremum-seeking controller that uses first-order least-squares fits if the plant is static.…”

“…It is shown in [12] that asymptotic convergence to the optimal plant performance can be obtained with an extremum-seeking controller that uses first-order least-squares fits if the plant is static. Moreover, simulation results for a Hammerstein-type plant indicate that asymptotic convergence can also be obtained for certain dynamical plants.…”

Maximum Power Point Tracking Control of a Thermoelectric Generation System Using the Extremum Seeking Control Method

“…The dithering signal aids in reducing the electromagnetic interference in the system, hence improving the performance of the MPPT algorithm [32]. However, there are some extremum seeking controllers without dither in the extremum seeking loop but instead depend on the past data of the performance map to estimate the gradient of the performance map by means of a 1st-order least squares fit [33]. The dither-less ESC controllers allow for an asymptotic stability result, as opposed to practical stability in dither-based schemes and, therefore enables convergence to the optimal performance of the parameters.…”

A Retrofit Hierarchical Architecture for Real-Time Optimization and Control Integration

“…It has recently gained increased attention since the stability problem was proven by Krstic and Wang [9]. In recent years, there has been several advancements in ESC approaches such as the least-square-based ESC [10,11], discrete-time ESC [12], sliding-mode ESC [13], Newton-based ESC [14], etc. A common step included in all of these approaches is to drive the estimated steady-state gradient to zero under some specific control law.…”