Extremum seeking control for an acceleration controlled unicycle

Abstract

We study the problem of source seeking with an acceleration controlled unicycle without position measurements. It is assumed that only real-time measurements of the source signal are available. The proposed control law is based on an approximation of the symmetric product of suitably chosen vector fields. The approximation of the symmetric product can be traced back to known averaging results for mechanical systems under vibrational control. Compared to known extremum seeking control laws by means of Lie bracket approximations, the proposed approach has the advantage that the velocity remains bounded in the high-frequency limit. We prove semi-global practical asymptotic stability for the acceleration-driven unicycle system under the proposed control law.