  Online Feedback Optimization is a method used to steer the operation of a
process plant to its optimal operating point without explicitly solving a
nonlinear constrained optimization problem. This is achieved by leveraging a
linear plant model and feedback from measurements. However the presence of
plant-model mismatch leads to suboptimal results when using this approach.
Learning the plant-model mismatch enables Online Feedback Optimization to
overcome this shortcoming. In this work we present a novel application of
Online Feedback Optimization with online model adaptation using Gaussian
Process regression. We demonstrate our approach with a realistic load sharing
problem in a compressor station with parametric and structural plant-model
mismatch. We assume imperfect knowledge of the compressor maps and design an
Online Feedback Optimization controller that minimizes the compressor station
power consumption. In the evaluated scenario, imperfect knowledge of the plant
leads to a 5\% increase in power consumption compared to the case with perfect
knowledge. We demonstrate that Online Feedback Optimization with model
adaptation reduces this increase to only 0.8%, closely approximating the case
of perfect knowledge of the plant, regardless of the type of mismatch.
