  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.
