DDE Model-Based Control of Glycemia via Sub-cutaneous Insulin Administration

Plasma glucose regulation is commonly attained in Type I Diabetes Mellitus (T1DM) patients, as well as in advanced Type 2 Diabetes Mellitus (T2DM), by means of Sub-Cutaneous (SC) insulin administration. In order to study this extremely common and relevant clinical problem from a theoretical point of view, a Delay Differential Equation (DDE) model of the glucose-insulin system has been considered. The model extends a previous DDE model, already used for glucose control, by endowing it with a SC Insulin compartment and by introducing modifications regarding insulin-independent glucose uptake and Hepatic Glucose Output (HGO). Pancreatic insulin release (non-negligible in T2DM) is considered, in order for the control method to address both T1DM and T2DM. The method of exact input/output feedback linearization and stabilization is used, to ensure the local convergence of the tracking error to zero. Numerical simulations show the effectiveness of the proposed approach.