Multivariable Recursive Subspace Identification with Application to Artificial Pancreas Systems

Abstract

Designing a fully automated artificial pancreas (AP) system is challenging. Changes in the glucose-insulin dynamics in the human body over time, and the inter-subject and day-to-day variability of people with type 1 diabetes (T1D) are two important factors that would highly undermine the performance of an AP that is based on time-invariant and non-individualized models. People with T1D show different responses to carbohydrate intake, insulin, physical activity and stress with day-to-day variability present between or within specific patients. Thus, the control law in an AP system requires a reliable time-varying individualized model to perform efficiently. In this work, a novel recursive identification approach called a Predictor-Based Subspace Identification (PBSID) method is used for identifying a linear time-varying glucose-insulin model for each individual. Model identification and validation are based on clinical data from closed-loop experiments. The models are evaluated by means of various performances indices: Variance Accounted For (VAF), Root mean square error (RMSE), Normalized root mean square error (NRMSE) and Normalized mean square error (NMSE). The proposed method provides a stable time-varying state space model over time. It can be also individualized for each patient by defining the order of the system correctly. The approach proposed in this work has shown a strong potential to identify a consistent glucose-insulin model in real time for use in an AP system.