  Grid-interfacing inverters act as the interface between renewable resources
and the electric grid, and have the potential to offer fast and programmable
controls compared to synchronous generators. With this flexibility there has
been significant research efforts into determining the best way to control
these inverters. Inverters are limited in their maximum current output in order
to protect semiconductor devices, presenting a nonlinear constraint that needs
to be accounted for in their control algorithms. Existing approaches either
simply saturate a controller that is designed for unconstrained systems, or
assume small perturbations and linearize a saturated system. These approaches
can lead to stability issues or limiting the control actions to be too
conservative.
  In this paper, we directly focus on a nonlinear system that explicitly
accounts for the saturation of the current magnitude. We use a Lyapunov
stability approach to determine a stability condition for the system,
guaranteeing that a class of controllers would be stabilizing if they satisfy a
simple SDP condition. With this condition we fit a linear-feedback controller
by sampling the output (offline) model predictive control problems. This
learned controller has improved performances with existing designs.
