Regulation of the Human Plasma Glycemia by Means of Glucose Measurements and Subcutaneous Insulin Administration

A glucose control problem is considered, with the aim to regulate a basal hyperglycemic state down to a safe euglycemic level. A discrete Delay Differential Equation (DDE) model of the glucose-insulin system is considered, that properly takes into account also the pancreatic insulin release, not negligible in Type 2 diabetic patients. Insulin is supposed to be administered subcutaneously. A geometric approach is considered, according to which the feedback linearization with delay cancelation theory is applied. In order to use only glucose measurements to synthesize the control law an observer for nonlinear delay systems is exploited, and the local convergence of the tracking error to zero is theoretically proven. Simulations are performed in a virtual environment, that properly takes into account input saturation: numerical results show the effectiveness of the proposed approach as well as that of the observer