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.

Devising optimal operating strategies for a compressor station relies on the knowledge of compressor characteristics. As the compressor characteristics change with time and use, it is necessary to provide accurate models of the characteristics that can be used in optimization of the operating strategy. This paper proposes a new algorithm for online learning of the characteristics of the compressors using Gaussian Processes. The performance of the new approximation is shown in a case study with three compressors. The case study shows that Gaussian Processes accurately capture the characteristics of compressors even if no knowledge about the characteristics is initially available. The results show that the flexible nature of Gaussian Processes allows them to adapt to the data online making them amenable for use in real-time optimization problems.