Blood glucose concentration regulation in Type 1 diabetics using multi model multi parametric model predictive control: An empirical approach

A Glucose- Insulin steady state static map is obtained from the Hovorka's 8th order virtual patient model. Three First Order Plus Time Delay (FOPTD) models are derived for the three piecewise linear regions in it. Through polyhedral vector space partitioning based on constraint violation, critical regions in state vector space are identified. A state feedback gain based controller is designed for each critical region. The controller design prevents constraint violations and ensures convexity while regulating the state vector to origin. The solution is also globally minimal. The state vector space of each empirical model is subjected to such analysis, resulting in three different set of critical regions and corresponding controllers. Gain Scheduling (GS) based on the Blood Glucose Concentration (BGC) measurement ensured proper profile selection. Through delay time compensation techniques, the multi model multi-parametric Model Predictive Control (mp-MPC) is designed for pure dynamics of each linear region. It is observed that the gain scheduled controller regulates the BGC within the acceptable range (80mg/dL to 160 mg/dL) during multiple meal disturbances. The explicit state feedback gain nature of the controller implies ease of deployment on memory constrained embedded devices.