Title: Extremum seeking for stabilization

Abstract: Extremum Seeking (ES) has a long history as a tool for
optimization of unknown output functions for dynamic systems. In this
talk, by utilizing the optimization properties of the ES algorithm for
minimization of Lyapunov functions, we present an ES scheme for
stabilization of unknown and possibly open loop unstable dynamic
systems. Our stability analysis is inspired by the recent approach of
Durr, Stankovic, and Johansson. We start by introducing Lie bracket
averaging techniques of Gurvits and Li, as well as perturbation
results of Moreau and Aeyels, to demonstrate semi-global exponential
practical stabilization of a large class of nonlinear and time-varying
systems. In particular, for the linear case we demonstrate that the ES
scheme is able to stabilize systems with unknown and persistently
changing control directions. Along with various simulation results we
present experimental results, conducted at Los Alamos National
Laboratory, in which the proposed algorithm was used to iteratively
optimize the output voltage of a High Voltage Converter Modulator.