Luenberger-like observers for nonlinear time-delay systems with application to the Articial Pancreas: the attainment of good performance

This article reviews results concerning Luenberger-like observers for nonlinear dynamical systems with state and output delays and their application to the problem of the real-time reconstruction of the insulinemia in humans from plasma glucose measurements is presented. The problem of obtaining the insulinemia by processing glycemia measurements is very important for the development of the AP, a device aimed at supporting or replacing the pancreatic activity of insulin production in diabetic individuals. Indeed, glycemia can be accurately, easily, and quickly measured by small, portable, and cheap devices, while insulinemia measurements require large and costly laboratory equipment. Asymptotic state observers can solve the problem of obtaining insulinemia from glycemia by suitably exploiting the mathematical model of glucose-insulin dynamics. A simple and accurate model available in the literature is in the form of a DDE and has already been successfully used for the construction of insulin observers as well as for designing an insulin-infusion therapy for T2DM patients.