Dynamic Mode Decomposition for Individualized Model Predictive Control with Application to Type 1 Diabetes

Type 1 diabetes is one of the main issues in current medical research. If not properly managed, it can lead to serious long-term complications such as blindness, stroke, coma and, ultimately, death. In recent years, research endeavors have focused on the development of a fully automated system for glucose control through automated insulin injections, known as Artificial Pancreas, which, however, is not yet robust enough for practical use. Currently, the UVA/Padova simulator provides the most accurate model for effectively representing the insulin-glucose dynamics of individual diabetic patients. As it is highly complex, consisting of 18 strongly nonlinear and time-varying equations, the objective of this work is to linearize it and reduce its dimensionality exploiting Dynamic Mode Decomposition with Control. This allows for the synthesis of a controller based on Linear Model Predictive Control to be applied to the original model. This is justified by the need to integrate the control algorithm into portable devices with limited computational capabilities. The proposed dimensionality reduction method is validated through in-vitro simulations showing that an accurate representation of the system dynamics is effectively preserved, while conveniently reducing required computational power.