Time-Delay Model-Based Control of the Glucose–Insulin System, by Means of a State Observer

Abstract

The problem of tracking a desired plasma glucose evolution is considered, for cases of basal hyperglycemia. A time-delay model is used to describe the glucose–insulin regulatory system, aiming to detail the endogenous pancreatic insulin release, which is not negligible in Type 2 diabetic patients. Insulin is assumed to be administered by means of intra-venous infusions. Only measurements of glycemia are considered: to this aim a nonlinear observer for time-delay systems is used to estimate the plasma insulin concentration. In the spirit of the separation theorem, a nonlinear control law is proposed, based on the exact input/output feedback linearization, which makes use of the observer estimates instead of the full state measurements. The local convergence of the tracking error to zero is theoretically proved. Simulations are performed in a virtual environment, taking into account the standard technology concerning blood glucose sensors and insulin delivery devices. Numerical results show the robustness of the proposed approach with respect to the uncertainties of the model parameters, as well as to the glucose measurement errors and insulin pump malfunctioning.