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

Abstract

Abstract-We introduce a perturbation-based extremumseeking controller for general nonlinear dynamical plants with an arbitrary number of tunable plant parameters. The controller ensures asymptotic convergence of the plant parameters to their performance-optimizing values for any initial plant condition under the assumptions in this work. The key to this result is that the amplitude and the frequencies of the perturbations, as well as other tuning parameters of the controller, are time varying. Remarkably, the time-varying tuning parameters can be chosen such that asymptotic convergence is achieved for all plants that satisfy the assumptions, thereby guaranteeing stability of the resulting closed-loop system of plant and controller regardless of tuning.

Dither signal optimization for multi-agent extremum seeking control

“…The gradient estimation has a central role in the ESC scheme since both the dither signal optimizer and the steadystate optimizer rely on accurate gradient estimates to function properly. Many perturbation-based ESC schemes utilize dynamic estimators such as band-pass filters [17] and observers [18] for gradient estimation. In order to avoid the interplay between the dither signal excitations and the estimation, we chose to use a static filter for gradient estimation.…”

Extremum seeking control of nonlinear dynamic systems using Lie bracket approximations

“…In general, for dynamic extremum seeking systems, a singular perturbation approach is quite common, see, for example, the articles. 2,4,11,17,33,34 In this article, however, we propose an alternative approach without singular perturbation theory using the techniques developed in Reference 16. In article 16, we extended the results of Reference 9 and gave a rather general description for a whole family of extremum seeking control laws.…”

Model‐based vs data‐driven adaptive control: An overview

“…Their basic goal is to seek an extremum, ie, maximize (or minimize), of a given function without closed‐from knowledge of the function or its gradient. There have been a lot of results on ES algorithms,) following the appearance of a rigorous convergence analysis in the work of Krstić and Wang …”