Extremum Seeking With Intermittent Measurements: A Lie-Brackets Approach

Extremum seeking systems are powerful methods able to steer the input of a (dynamical) cost function toward an optimizer, without any prior knowledge of the cost function. To achieve their objective, they typically combine time-periodic signals with the online 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 article, 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.