Koopman Linearization and Optimal Control of Glucose Level

The Artificial Pancreas Problem (APP) offers a potential framework for Control Engineering studies, specifically in the field of continuous monitoring and actuation to control glucose levels. The models that give a satisfactory level of accuracy are nonlinear by nature however, the standard approach in linear control is to find a linear representation of the model. The current paper proposes a comparison between standard linearization and linearization via the Koopman Operator for an input-affine nonlinear model from insulin intake to glucose level. Each model also has an additive disturbance component. To account for it, the current paper proposes a method of modeling the disturbance based on Gauss Processes. For a meaningful comparison between the considered linear matrix inequality-based controllers (LMI) and linear-quadratic regulators (LQR), the paper introduces the term Glucose Absolute Error (GAE) as an error index adapted for the Insulin-Glucose system.