Luenberger-like Observers for Nonlinear Time-Delay Systems with Application to the Artificial Pancreas

This article reviews results concerning Luenberger-like observers for nonlinear dynamical systems with state and output delays. The aim of this article is to show the good performance obtained by the state observer applied to a DDE model of the glucose-insulin system recently used in the AP framework. The use of observers as a subsystem in AP appears to be a promising technique, although some work has still to be done, in particular, for the development of observers that deal with DDE models and sampled measurements. Validation is carried out by real clinical measurements available from 20 healthy subjects who underwent an intravenous glucose tolerance test. The problem of state estimation when output measurements are available after some delay arises frequently in engineering applications. The AP refers to the set of glucose control strategies required for diabetic people and wherein glucose is controlled by exogenous insulin administration, usually via subcutaneous or intravenous infusions.