Extremum seeking control with an adaptive dither signal

Abstract

We present an output-feedback law that steers a fully actuated control-affine system with general drift vector field to a minimum of the output function. The proposed control law is based on a suitable approximation of descent directions by Lie brackets in the high-frequency limit. A novelty of our approach is an adaptive choice of the frequency parameter. In this way, the problem of determining a sufficiently large frequency parameter becomes obsolete. The adaptive choice of the frequency parameter also prevents finite escape times in the presence of a drift. The proposed control law does not only lead to convergence into a neighborhood of the set of minima, but leads to exact convergence. For the case of an output function with a global minimum and no other stationary points, we prove global convergence.