Asymptotic stability of perturbation-based extremum-seeking control for nonlinear plants

Abstract

Abstract—We introduce a perturbation-based extremum-seeking controller for general nonlinear dynamical plants withan arbitrary number of tunable plant parameters. The controllerensures asymptotic convergence of the plant parameters to theirperformance-optimizing values for any initial plant conditionunder the assumptions in this work. The key to this result isthat the amplitude and the frequencies of the perturbations,as well as other tuning parameters of the controller, are timevarying. Remarkably, the time-varying tuning parameters can bechosen such that asymptotic convergence is achieved for all plantsthat satisfy the assumptions, thereby guaranteeing stability of theresulting closed-loop system of plant and controller regardless oftuning.