Kernel-Based Identification of Local Limit Cycle Dynamics with Linear Periodically Parameter-Varying Models

TL;DR

This paper introduces a kernel-based method to identify local limit cycle dynamics in nonlinear systems using linear periodically parameter-varying models, with applications demonstrated on benchmark and wind energy models.

Contribution

It presents a novel kernel-based identification approach for local limit cycle dynamics, incorporating parameter variations for different operating conditions.

Findings

Accurate model parameter estimation compared to analytical linearization

Good prediction capability demonstrated on benchmark systems

Effective handling of parameter variations in system dynamics

Abstract

Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be modelled as systems experiencing limit cycle behavior. The goal of this work is to identify from data, the local dynamics around the limit cycle using linear periodically parameter-varying models. Using a coordinate transformation onto transversal surfaces, the dynamics are decomposed into two parts: one along the limit cycle, and one on the transversal surfaces. Then, the model is identified from trajectory data using kernel-based methods with a periodic kernel design. The kernel-based model is extended to also account for variations in system parameters associated with different operating conditions. The performance of the proposed identification method is demonstrated on a benchmark nonlinear system and on a simplified airborne wind energy model. The method provides accurate model parameter estimation, compared to the analytical linearization, and good prediction capability.