Data-Driven Koopman-Enhanced Extremum Seeking for Oscillation Damping in Nonlinear Systems

TL;DR

This paper introduces a Koopman-based extremum seeking control method that enhances oscillation damping in nonlinear systems by operating in a lifted linear state space, leading to faster and more robust performance.

Contribution

The novel approach combines Koopman operator theory with extremum seeking control to improve damping efficiency in nonlinear oscillatory systems.

Findings

Faster convergence in damping oscillations compared to traditional methods.

More robust performance under time-varying and nonlinear conditions.

Effective in applications like vibration suppression and power system stability.

Abstract

We propose a novel extremum seeking control (ESC) method that operates in a lifted Koopman state space to minimize the filtered RMS energy in the dominant subspace. The lifted representation provides linear embeddings of nonlinear dynamics, enabling more accurate gradient estimation and dampening of state interference for more consistent ESC performance. Applied to a parameterized, forced, and time-varying Van der Pol oscillator, we show that the approach yields faster and more robust performance than operating ESC on the measured states. These advantages position the method for a diverse range of applications including vibration suppression, motion control, and subsynchronous oscillation mitigation in inverter-dominated power systems.