Extremum Seeking with Intermittent Measurements: A Lie-brackets Approach

TL;DR

This paper investigates extremum seeking control with intermittent measurements, analyzing existing Lie-bracket methods and proposing modifications to enhance convergence and accuracy under practical measurement constraints.

Contribution

It introduces two modified Lie-bracket extremum seeking schemes tailored for intermittent measurements, improving convergence speed and steady-state accuracy.

Findings

Modified schemes outperform classical methods with intermittent data

Proposed methods achieve faster convergence

Steady-state accuracy is improved

Abstract

Extremum seeking systems are powerful methods able to steer the input of a (dynamical) cost function towards an optimizer, without any prior knowledge of the cost function. To achieve their objective, they typically combine time-periodic signals with the on-line measurement of the cost. However, in some practical applications, the cost can only be measured during some regular time-intervals, and not continuously, contravening the classical extremum seeking framework. In this paper, we first analyze how existing Lie-bracket based extremum seeking systems behave when being fed with intermittent measurements, instead of continuous ones. We then propose two modifications of those schemes to improve both the convergence time and the steady-state accuracy in presence of intermittent measurements. The performances of the different schemes are compared on a case study.