Robustness properties of a large-amplitude, high-frequency extremum seeking control scheme

TL;DR

This paper investigates the stability and robustness of a high-frequency extremum seeking control scheme with large-amplitude oscillations, considering disturbances and showing ISS-like properties through averaging techniques.

Contribution

It provides a theoretical analysis demonstrating that stability and robustness properties of the averaged system extend to the actual extremum seeking scheme under certain conditions.

Findings

Closed-loop system approximates averaged system behavior.

Stability and robustness carry over from averaged to actual system.

ISS-like properties are established for the closed-loop system.

Abstract

We analyze stability and robustness properties of an extremum seeking scheme that employs oscillatory dither signals with sufficiently large amplitudes and frequencies. Our study takes both input and output disturbances into account. We consider general $L_\infty$-disturbances, which may resonate with the oscillatory dither signals. A suitable change of coordinates followed by an averaging procedure reveals that the closed-loop system approximates the behavior of an averaged system. This leads to the effect that stability and robustness properties carry over from the averaged system to the closed-loop system. In particular, we show that, if the averaged system is input-to-state stable (ISS), then the closed-loop system has ISS-like properties.